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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-02-09</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001836337</issuerCik>
        <issuerName>Lazard Growth Acquisition Corp. I</issuerName>
        <issuerTradingSymbol>LGAC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001450474</rptOwnerCik>
            <rptOwnerName>Stern Alexander F.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O LAZARD GROWTH ACQUISITION CORP. I</rptOwnerStreet1>
            <rptOwnerStreet2>30 ROCKEFELLER PLAZA</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10112</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EXECUTIVE CHAIRMAN</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Series B Membership Interests</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class B Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>100000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">As described in the registration statement on Form S-1 (File No. 333-252408) of Lazard Growth Acquisition Corp. I, a Cayman Island exempted company (the &quot;Issuer&quot;), under the heading &quot;Principal Shareholders&quot;, the reporting person holds all of the limited liability company interests (the &quot;Series Membership Interests&quot;) in a series of LGACo 1 LLC, a Delaware series limited liability company and the Issuer's sponsor (the &quot;Sponsor&quot;), which entitles the reporting person to economic interests in respect of 100,000 Class B ordinary shares, par value $0.0001 per share (the &quot;Founder Shares&quot;). The Founder Shares will automatically convert into Class A ordinary shares, par value $0.0001 per share, of the Issuer at the time of the Issuer's initial business combination, or earlier at the option of the holder thereof, on a one-for-one basis, subject to adjustment for share sub-divisions, share capitalizations, reorganizations, recapitalizations and the like pursuant to certain anti-dilution rights.</footnote>
        <footnote id="F2">Pursuant to the amended and restated operating agreement of the Sponsor, Lazard Group LLC, a Delaware limited liability company, is the sole manager of the Sponsor and each series thereof and, accordingly, maintains the voting rights attributable to, and the dispositive power in respect of, all of the Founder Shares underlying the Series Membership Interests. LGA HoldCo LLC, a Delaware limited liability company and the Series A Member of the Sponsor, has full power to appoint, remove or replace the sole manager of the Sponsor at any time. The reporting person disclaims beneficial ownership of any such Founder Shares except to the extent of its pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Alexander F. Stern</signatureName>
        <signatureDate>2021-02-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
