<?xml version="1.0"?><?xml-stylesheet type="text/xsl" href="/Pages/Form4.xsl"?>
<ownershipDocument>

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-05-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001487999</issuerCik>
        <issuerName>SeaCube Container Leasing Ltd.</issuerName>
        <issuerTradingSymbol>BOX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000939713</rptOwnerCik>
            <rptOwnerName>TUCHMAN MARTIN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SEACUBE CONTAINER LEASING LTD.</rptOwnerStreet1>
            <rptOwnerStreet2>1 MAYNARD DRIVE</rptOwnerStreet2>
            <rptOwnerCity>PARK RIDGE</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>07656</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2011-05-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13499</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.9833</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>67872</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2011-05-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>16800</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.1499</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>84672</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents weighted average price of open market same day purchases. Purchases of shares took place at actual prices ranging from $15.90 to $16.10 per share.</footnote>
        <footnote id="F2">Full information regarding the number of shares purchased at each separate price will be provided upon request by the Commission staff, SeaCube Container Leasing Ltd. or a SeaCube Container Leasing Ltd. shareholder.</footnote>
        <footnote id="F3">Represents weighted average price of open market same day purchases. Purchases of shares took place at actual prices ranging from $16.1495 to $16.15 per share.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Lisa Leach, as attorney-in-fact</signatureName>
        <signatureDate>2011-05-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
