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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-03-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001348649</issuerCik>
        <issuerName>CoLucid Pharmaceuticals, Inc.</issuerName>
        <issuerTradingSymbol>CLCD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000059478</rptOwnerCik>
            <rptOwnerName>LILLY ELI &amp; CO</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>LILLY CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INDIANAPOLIS</rptOwnerCity>
            <rptOwnerState>IN</rptOwnerState>
            <rptOwnerZipCode>46285</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001695312</rptOwnerCik>
            <rptOwnerName>ProCar Acquisition Corp</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>LILLY CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>INDIANAPOLIS</rptOwnerCity>
            <rptOwnerState>IN</rptOwnerState>
            <rptOwnerZipCode>46285</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.001</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2017-03-01</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>19285108</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>46.50</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On March 1, 2017, Eli Lilly and Company (&quot;Parent&quot;) and ProCar Acquisition Corporation (&quot;Merger Sub&quot;) completed the transactions contemplated by the Agreement and Plan of Merger, dated as of January 17, 2017, by and among CoLucid Pharmaceuticals, Inc. (the &quot;Issuer&quot;), Parent and Merger Sub (the &quot;Merger Agreement&quot;).  Pursuant to the terms of the Merger Agreement, Merger Sub merged with and into the Issuer (the &quot;Merger&quot;), with the Issuer surviving the Merger as a wholly-owned subsidiary of Parent (the &quot;Surviving Corporation&quot;).  At the effective time of the Merger, the outstanding shares of common stock of Merger Sub were converted into and became shares of the Surviving Corporation.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Derica W. Rice, Executive Vice President and CFO, Eli Lilly and Company</signatureName>
        <signatureDate>2017-03-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Darren J. Carroll, President, ProCar Acquisition Corporation</signatureName>
        <signatureDate>2017-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
