Searches for Weakly Interacting Massive Particles (WIMPs) carried out by liquid xenon time projection chambers (TPCs) require a careful accounting of all background sources. Because WIMPs are a leading dark matter candidate, their possible existence is of great interest to particle physicists, astrophysicists, and cosmologists. The LUX-ZEPLIN (LZ) detector has completed an initial science run finding no evidence for WIMP scattering events. The data excludes scattering cross sections above 6.5x10$^{-48}$ cm$^{2}$ for a WIMP mass of 30 GeV/c$^{2}$. Background contributions from the beta decay of dispersed \isotope[85]{Kr} were reduced prior to the initial science run using charcoal chromatography to remove trace krypton. Over 10 tonnes of xenon were processed, and a custom mass spectrometry system measured a final mass averaged krypton concentration of 123 $\pm$ 22 parts-per-quadrillion (ppq) $\frac{gram}{gram}$ $\frac{ \isotope[nat]{Kr} }{\isotope[nat]{Xe}}$. A delayed coincidence $\beta$ - $\gamma$ search was also conducted to identify rare decays from \isotope[85]{Kr} in the LZ WIMP search data. The 11.0 $\pm$ 4.0 identified events are equivalent to a concentration of 183 $\pm$ 67 ppq. The total background contribution from \isotope[85]{Kr} to the WIMP search region of interest is 30 $ \pm $ 11 electron recoil events.