<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>0208 - Disclosure - Long-Term Debt</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2011 - 3/31/2011
USD ($)

USD ($) / shares

</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>ThreeMonthsEnded_31Mar2011</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001424847</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2011-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2011-03-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>Shares</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>USDEPS</UnitID><UnitType>Divide</UnitType><NumeratorMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></NumeratorMeasure><DenominatorMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></DenominatorMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>Pure</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>pure</MeasureValue><MeasureNamespace>xbrli</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="3 Months Ended" /><Label Id="2" Label="Mar. 31, 2011" /></Labels></Column></Columns><Rows><Row><Id>2</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_LongTermDebtAbstract</ElementName><ElementPrefix>us-gaap</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>No definition available.</ElementDefenition><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Long-Term Debt [Abstract]</Label></Row><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>us-gaap_LongTermDebtTextBlock</ElementName><ElementPrefix>us-gaap</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>No definition available.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>
    &lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
    &lt;!-- Begin Block Tagged Note 8 - us-gaap:LongTermDebtTextBlock--&gt;
    &lt;div style="font-family: 'Times New Roman',Times,serif"&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt; margin-left: 1%"&gt;&lt;b&gt;8. Long-Term Debt&lt;/b&gt;
    &lt;/div&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;Long-term debt, net of interest rate swaps, consisted of the following:
    &lt;/div&gt;
    &lt;div align="center"&gt;
    &lt;table style="font-size: 10pt; text-align: left" cellspacing="0" border="0" cellpadding="0" width="100%"&gt;
    &lt;!-- Begin Table Head --&gt;
    &lt;tr valign="bottom"&gt;
    &lt;td width="76%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="1%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="1%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="1%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="5%"&gt;&amp;#160;&lt;/td&gt;
    &lt;td width="1%"&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 8pt" valign="bottom"&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="2"&gt;March 31,&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="2"&gt;December 31,&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 8pt" valign="bottom"&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="2" style="border-bottom: 1px solid #000000"&gt;2011&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="2" style="border-bottom: 1px solid #000000"&gt;2010&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 8pt" valign="bottom"&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" align="center" colspan="6"&gt;(In millions)&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;!-- End Table Head --&gt;
    &lt;!-- Begin Table Body --&gt;
    &lt;tr valign="bottom" style="background: #cceeff"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;2019 Notes &amp;#8211; 8.125% Notes due 2019
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left"&gt;$&lt;/td&gt;
    &lt;td align="right"&gt;759&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left"&gt;$&lt;/td&gt;
    &lt;td align="right"&gt;769&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;2020 Notes &amp;#8211; 6.875% Notes due 2020
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;750&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;750&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom" style="background: #cceeff"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;2040 Notes &amp;#8211; 8.125% Notes due 2040
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;250&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="right"&gt;250&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 1px"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;&amp;#160;
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="2" align="right" style="border-top: 1px solid #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="2" align="right" style="border-top: 1px solid #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:30px; text-indent:-15px"&gt;Total long-term debt
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left"&gt;$&lt;/td&gt;
    &lt;td align="right"&gt;1,759&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td align="left"&gt;$&lt;/td&gt;
    &lt;td align="right"&gt;1,769&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr style="font-size: 1px"&gt;
    &lt;td&gt;
    &lt;div style="margin-left:15px; text-indent:-15px"&gt;&amp;#160;
    &lt;/div&gt;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="2" align="right" style="border-top: 3px double #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;td nowrap="nowrap" colspan="2" align="right" style="border-top: 3px double #000000"&gt;&amp;#160;&lt;/td&gt;
    &lt;td&gt;&amp;#160;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;!-- End Table Body --&gt;
    &lt;/table&gt;
    &lt;/div&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;In April&amp;#160;2010, Lorillard Tobacco issued $1&amp;#160;billion of unsecured senior notes in two tranches
    pursuant to an Indenture, dated June&amp;#160;23, 2009, and the Second Supplemental Indenture, dated April
    12, 2010 (the &amp;#8220;Second Supplemental Indenture&amp;#8221;). The first tranche was $750&amp;#160;million aggregate
    principal amount of 6.875% Notes due May&amp;#160;1, 2020 (the &amp;#8220;2020 Notes&amp;#8221;), and the second tranche was
    $250&amp;#160;million aggregate principal amount of 8.125% Notes due May&amp;#160;1, 2040 (the &amp;#8220;2040 Notes&amp;#8221;). The
    net proceeds from the issuance will be used for general corporate purposes, which may include,
    among other things, the repurchase, redemption or retirement of securities including the Company&amp;#8217;s
    common stock, acquisitions, additions to working capital and capital expenditures.
    &lt;/div&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;In June&amp;#160;2009, Lorillard Tobacco issued $750&amp;#160;million aggregate principal amount of 8.125%
    unsecured senior notes due June&amp;#160;23, 2019 (the &amp;#8220;2019 Notes&amp;#8221;) pursuant to an Indenture, dated June
    23, 2009, and First Supplemental Indenture, dated June&amp;#160;23, 2009 (the &amp;#8220;First Supplemental
    Indenture&amp;#8221;).
    &lt;/div&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;Lorillard Tobacco is the principal, wholly-owned operating subsidiary of the Company; and the
    2019 Notes, 2020 Notes and 2040 Notes (together, the &amp;#8220;Notes&amp;#8221;) are unconditionally guaranteed on a
    senior unsecured basis by the Company.
    &lt;/div&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;The interest rate payable on the 2019 Notes is subject to incremental increases from 0.25% to
    2.00% in the event either Moody&amp;#8217;s Investors Services, Inc. (&amp;#8220;Moody&amp;#8217;s&amp;#8221;), Standard &amp;#038; Poor&amp;#8217;s Ratings
    Services (&amp;#8220;S&amp;#038;P&amp;#8221;) or both Moody&amp;#8217;s and S&amp;#038;P downgrade the 2019 Notes below investment grade (Baa3 and
    BBB- for Moody&amp;#8217;s and S&amp;#038;P, respectively). As of March&amp;#160;31, 2011, our debt ratings were Baa2 and BBB-
    with Moody&amp;#8217;s and S&amp;#038;P, respectively, both of which are investment grade.
    &lt;/div&gt;
    &lt;div align="left" style="font-size: 10pt; margin-top: 6pt"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;Upon the occurrence of a change of control triggering event, Lorillard Tobacco would be
    required to make an offer to repurchase the Notes at a price equal to 101% of the aggregate
    principal amount of the Notes, plus accrued interest. A &amp;#8220;change of control triggering event&amp;#8221;
    occurs when there is both a &amp;#8220;change of control&amp;#8221; (as defined in the Supplemental Indentures) and the
    Notes cease to be rated investment grade by both Moody&amp;#8217;s and S&amp;#038;P within 60&amp;#160;days of the occurrence
    of a change of control or public announcement of the intention to effect a change of control. The
    Notes are not entitled to any sinking fund and are not redeemable prior to maturity. The Notes
    contain covenants that restrict liens and sale and leaseback transactions, subject to a limited
    exception. At March&amp;#160;31, 2011 and December&amp;#160;31, 2010, the carrying value of the Notes was $1.759
    billion and $1.769&amp;#160;billion, respectively, and the fair value was $1.956&amp;#160;billion and $1.865&amp;#160;billion,
    respectively. The fair value of the Notes is based on market pricing.
    &lt;/div&gt;
    &lt;/div&gt;
  </NonNumbericText><NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
    &lt;!-- Begin Block Tagged Note</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>This element may be used as a single block of text to encapsulate the entire disclosure for long-term borrowings including data and tables.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 02
 -Paragraph 22
 -Article 5

</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Long-Term Debt</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>Long-Term Debt</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
