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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2019-03-28</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001757898</issuerCik>
        <issuerName>STERIS Ltd</issuerName>
        <issuerTradingSymbol>STE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001237389</rptOwnerCik>
            <rptOwnerName>WILSON LOYAL W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 70 SIR JOHN ROGERSON'S QUAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DUBLIN</rptOwnerCity>
            <rptOwnerState>L2</rptOwnerState>
            <rptOwnerZipCode>2</rptOwnerZipCode>
            <rptOwnerStateDescription>IRELAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Exhibit 24-Power of Attorney Reflects the beneficial ownership of the reporting person at the time of his appointment as a reporting person of STERIS plc, a public limited company organized under the laws of Ireland (&quot;STERIS Ireland&quot;), and does not include the securities acquired by the reporting person upon the consummation of the redomiciliation of STERIS plc, a public limited company organized under the laws of England and Wales, pursuant to a court-approved scheme of arrangement (the &quot;Scheme&quot;) on March 28, 2019. The reporting person will file a Form 4 reflecting his acquisition of STERIS Ireland securities in connection with the consummation of the Scheme.</remarks>

    <ownerSignature>
        <signatureName>/s/ Ronald E. Snyder, Authorized Representative under Power of Attorney</signatureName>
        <signatureDate>2019-03-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
