<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-03-20</periodOfReport>

    <issuer>
        <issuerCik>0001069202</issuerCik>
        <issuerName>LENNOX INTERNATIONAL INC</issuerName>
        <issuerTradingSymbol>LII</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001703854</rptOwnerCik>
            <rptOwnerName>Kosel Chris</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2140 LAKE PARK BLVD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>RICHARDSON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75080</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isOfficer>1</isOfficer>
            <officerTitle>VP-Corp Controller and CAO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, Par Value $0.01 Per Share</value>
            </securityTitle>
            <transactionDate>
                <value>2019-03-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>416</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>252.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1027</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This sale was effected pursuant to a Rule 10b5-1 trading plan.</footnote>
    </footnotes>

    <remarks>Attorney-in-fact pursuant to power of attorney dated December 6, 2017.</remarks>

    <ownerSignature>
        <signatureName>/s/ Sarah Braley, attorney-in-fact for Mr. Kosel</signatureName>
        <signatureDate>2019-03-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
