Currently, one of the most well motivated models of dark matter is the weakly inter- acting massive particle (WIMP), and the detector technology that is in the best position to observe these WIMPs is the two-phase liquid xenon time projection chamber (TPC). As liquid xenon WIMP detectors grow larger and more sensitive, the requirements placed on their signals and backgrounds become more and more stringent. We develop a technique for measuring the concentration of the radioactive 85Kr isotope in xenon. We show that we are able to detect natural krypton concentrations down to 7.7 ±2.0 parts per quadrillion (ppQ). On the signals side, we provide a measurement of the charge and light yields of beta recoils in liquid xenon. For these measurements, we use 14C and 3H calibration data col- lected in the LUX detector after the 2014-2016 WIMP-search run was completed. These measurements span from 43 to 491 V/cm in electric field and from 1 to 140 keVee in recoil energy. We also look for a non-statistical shape factor in the 14C spectrum. We observe a spectrum in the LUX data that is consistent with a purely statistical shape, which disagrees with a recent measurement by Kuzminov et al. by 1.8σ . However, pathologies in the LUX signals prevent us from making any strong claims on this topic.