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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-07-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000023666</issuerCik>
        <issuerName>LEE SARA CORP</issuerName>
        <issuerTradingSymbol>SLE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001053288</rptOwnerCik>
            <rptOwnerName>WILLIE DAVIS</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>161 N. LA BREA AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INGLEWOOD</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90301</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>common stock</value>
            </securityTitle>
            <transactionDate>
                <value>2005-07-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4020</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>19.595</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>44006</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Consists of restricted stock units granted for serving on the Board of Directors, and on one or more Committees of the Board, during fiscal year 2006.  The restricted stock units will vest on June 30, 2006 and will be converted into shares of Sara Lee common stock on a one-for-one basis on the date six months after the reporting person ceases to be a director of Sara Lee.</footnote>
        <footnote id="F2">Includes 11,280 RSUs that may be settled only for shares of common stock. RSUs vest one year after the grant date and, on the settlement date, are convertible into shares of common stock on a one-for-one basis.  The settlement date is either three years after the date of grant, for RSUs granted before July 2005, or six months after the reporting person ceases to be a director of Sara Lee, for other RSUs.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Helen N. Kaminski
For Willie D. Davis pursuant to power of attorney previously filed.</signatureName>
        <signatureDate>2005-07-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
