  The LUX-ZEPLIN experiment recently reported limits on WIMP-nucleus
interactions from its initial science run, down to $9.2\times10^{-48}$ cm$^2$
for the spin-independent interaction of a 36 GeV/c$^2$ WIMP at 90% confidence
level. In this paper, we present a comprehensive analysis of the backgrounds
important for this result and for other upcoming physics analyses, including
neutrinoless double-beta decay searches and effective field theory
interpretations of LUX-ZEPLIN data. We confirm that the in-situ determinations
of bulk and fixed radioactive backgrounds are consistent with expectations from
the ex-situ assays. The observed background rate after WIMP search criteria
were applied was $(6.3\pm0.5)\times10^{-5}$ events/keV$_{ee}$/kg/day in the
low-energy region, approximately 60 times lower than the equivalent rate
reported by the LUX experiment.
