<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2024 Workiva-->
<!--r:630f2791-75fe-4ef0-987c-4dca3147940b,g:294efb8a-920e-4886-b1b0-bddea3fe5062-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.livanova.cyberonics.com/role/DocumentandEntityInformationDocument" xlink:type="simple" xlink:href="livn-20240611.xsd#DocumentandEntityInformationDocument"/>
  <link:presentationLink xlink:role="http://www.livanova.cyberonics.com/role/DocumentandEntityInformationDocument" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_8d8f45bd-0162-4858-9cd1-5a9edf2c9411" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_DocumentType_8d8f45bd-0162-4858-9cd1-5a9edf2c9411" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_6a26bf36-accc-4812-9a71-16bb23ebfe31" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_DocumentPeriodEndDate_6a26bf36-accc-4812-9a71-16bb23ebfe31" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_52f180d8-ea73-4205-9174-d4d140c0cd9f" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityIncorporationStateCountryCode_52f180d8-ea73-4205-9174-d4d140c0cd9f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_d2acf10f-b07a-4161-a5d8-2d1c67a721f0" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityFileNumber_d2acf10f-b07a-4161-a5d8-2d1c67a721f0" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_e6ccdfd5-3a26-4213-a57d-1abdc210c7d8" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityTaxIdentificationNumber_e6ccdfd5-3a26-4213-a57d-1abdc210c7d8" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_135ae5fe-0b85-42f6-aa7f-96dd07f93944" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityAddressAddressLine1_135ae5fe-0b85-42f6-aa7f-96dd07f93944" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_2789e871-5927-4ded-9a7b-ecd43779dea9" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityAddressCityOrTown_2789e871-5927-4ded-9a7b-ecd43779dea9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_c5c6aa82-e279-455e-af44-3af751a6d03e" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityAddressPostalZipCode_c5c6aa82-e279-455e-af44-3af751a6d03e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry_5d297158-3f53-415f-8642-19b04e80ae2b" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCountry"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityAddressCountry_5d297158-3f53-415f-8642-19b04e80ae2b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CountryRegion_1c57acd8-6456-4af9-a338-78267bca67f6" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CountryRegion"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_CountryRegion_1c57acd8-6456-4af9-a338-78267bca67f6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_16bf5dc4-f02f-473b-8d6a-ed41bf9933e6" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_CityAreaCode_16bf5dc4-f02f-473b-8d6a-ed41bf9933e6" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_7e832d7a-01ae-417e-8ed0-75a6f611ef31" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_LocalPhoneNumber_7e832d7a-01ae-417e-8ed0-75a6f611ef31" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_bb5ca775-17dc-4fec-9114-96e3e71beb76" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_WrittenCommunications_bb5ca775-17dc-4fec-9114-96e3e71beb76" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_49c07e19-f0c1-45f9-bc0c-56785eb063b0" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_SolicitingMaterial_49c07e19-f0c1-45f9-bc0c-56785eb063b0" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_487934c5-4031-4162-809c-4509d074f579" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_PreCommencementTenderOffer_487934c5-4031-4162-809c-4509d074f579" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_b2238638-3047-4144-af5d-b8a54c710822" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_b2238638-3047-4144-af5d-b8a54c710822" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_2ea22201-8750-4f1f-a81b-06019228969f" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_Security12bTitle_2ea22201-8750-4f1f-a81b-06019228969f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_5d51481c-ff9c-430e-ae5e-ab6e2c6f15c7" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_TradingSymbol_5d51481c-ff9c-430e-ae5e-ab6e2c6f15c7" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_738e57a0-7f03-4b8d-ba19-c9831926af4b" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_SecurityExchangeName_738e57a0-7f03-4b8d-ba19-c9831926af4b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_cf34a20e-0de6-43d2-bfeb-b9346f72a4de" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityEmergingGrowthCompany_cf34a20e-0de6-43d2-bfeb-b9346f72a4de" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_ee04b931-acc2-4c8d-bac3-3e4ae8e27e0b" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityRegistrantName_ee04b931-acc2-4c8d-bac3-3e4ae8e27e0b" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_9669256d-2aec-424e-b06d-d88bb5cfb7c9" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_EntityCentralIndexKey_9669256d-2aec-424e-b06d-d88bb5cfb7c9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_29db5d91-e5f8-47c3-aacb-f8ee5651f620" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_ada0dd3f-9c6d-495e-b02f-f21269bc1693" xlink:to="loc_dei_AmendmentFlag_29db5d91-e5f8-47c3-aacb-f8ee5651f620" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
