  The projected sensitivity of the LUX-ZEPLIN (LZ) experiment to two-neutrino
and neutrinoless double beta decay of $^{134}$Xe is presented. LZ is a 10-tonne
xenon time projection chamber optimized for the detection of dark matter
particles, that is expected to start operating in 2021 at Sanford Underground
Research Facility, USA. Its large mass of natural xenon provides an exceptional
opportunity to search for the double beta decay of $^{134}$Xe, for which xenon
detectors enriched in $^{136}$Xe are less effective. For the two-neutrino decay
mode, LZ is predicted to exclude values of the half-life up to
1.7$\times$10$^{24}$ years at 90% confidence level (CL), and has a three-sigma
observation potential of 8.7$\times$10$^{23}$ years, approaching the
predictions of nuclear models. For the neutrinoless decay mode LZ, is projected
to exclude values of the half-life up to 7.3$\times$10$^{24}$ years at 90% CL.
