Projected sensitivity of the LUX-ZEPLIN experiment to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0</mml:mn><mml:mi>ν</mml:mi><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math> decay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Xe</mml:mi><mml:mprescripts/><mml:none/><mml:mn>136</mml:mn></mml:mmultiscripts></mml:math>

The LUX-ZEPLIN (LZ) experiment will enable a neutrinoless double $\ensuremath{\beta}$ decay search in parallel to the main science goal of discovering dark matter particle interactions. We report the expected LZ sensitivity to $^{136}\mathrm{Xe}$ neutrinoless double $\ensuremath{\beta}$ decay, taking advantage of the significant ($&gt;600$ kg) $^{136}\mathrm{Xe}$ mass contained within the active volume of LZ without isotopic enrichment. After 1000 live-days, the median exclusion sensitivity to the half-life of $^{136}\mathrm{Xe}$ is projected to be $1.06\ifmmode\times\else\texttimes\fi{}{10}^{26}$ years (90% confidence level), similar to existing constraints. We also report the expected sensitivity of a possible subsequent dedicated exposure using 90% enrichment with $^{136}\mathrm{Xe}$ at $1.06\ifmmode\times\else\texttimes\fi{}{10}^{27}$ years.