<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>
<periodOfReport>2004-01-05</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0001219702</issuerCik>
        <issuerName>LINK ENERGY LLC</issuerName>
        <issuerTradingSymbol>LNKE</issuerTradingSymbol>
</issuer>
<reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000806085</rptOwnerCik>
            <rptOwnerName>LEHMAN BROTHERS HOLDINGS INC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>745 SEVENTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>0</isDirector>
<isOfficer>0</isOfficer>
<isTenPercentOwner>1</isTenPercentOwner>
<isOther>0</isOther>
<officerTitle></officerTitle>
<otherText></otherText>
</reportingOwnerRelationship>
</reportingOwner>
<nonDerivativeTable>
<nonDerivativeTransaction>
<securityTitle>
<value>Limited Liability Company Units</value>
</securityTitle>
<transactionDate>
<value>2004-01-05</value>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>J</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
<footnoteId id="F1"/>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>270995</value>
</transactionShares>
<transactionPricePerShare>
<footnoteId id="F1"/>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>A</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>2466851</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>See footnote</value>
<footnoteId id="F2"/>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
</nonDerivativeTable>
<footnotes>
<footnote id="F1">Received by Lehman Brothers Inc. on January 5, 2004, as a second distribution of Link Energy LLC&#039;s limited liability company units under Link Energy LLC&#039;s (formerly known as EOTT Energy LLC) Restructuring Plan dated March 1, 2003.</footnote>
<footnote id="F2">This form is a joint filing with Lehman Brothers Inc., a Broker-Dealer registered under Section 15 of the 1934 Act and a wholly-owned subsidiary of the Reporting Person, which is the actual owner of the limited liability company units reported herein.</footnote>
</footnotes>
<remarks>JOINT FILER INFORMATION

Title of Security:
Limited Liability Company Units
Issuer and Ticker Symbol:
Link Energy LLC (LNKE)
Designated Filer:
Lehman Brothers Holdings Inc.
Other Joint Filer:
Lehman Brothers Inc.
745 Seventh Avenue
New York, New York 10019
Date of Event Requiring Statement:
January 5, 2004
Signature on behalf of other above filer: /s/ Barrett S. DiPaolo, Senior Vice President
</remarks>
<ownerSignature>
<signatureName>/s/ Barrett S. DiPaolo</signatureName>
<signatureDate>2004-01-07</signatureDate>
</ownerSignature>
</ownershipDocument>

