  Knowledge of the ionization and scintillation responses of liquid xenon (LXe)
to nuclear recoils is crucial for LXe-based dark matter experiments. Current
calibrations carry large uncertainties in the low-energy region below $\sim3$
keV$_nr$ where signals from dark matter particles of $<$10 GeV/c$^2$ masses are
expected. The coherent elastic neutrino-nucleus scattering (CE$\nu$NS) by solar
$^8$B neutrinos also results in a continuum of nuclear recoil events below 3.0
keV$_{nr}$ (99\% of events), which further complicates low-mass dark matter
searches in LXe experiments. In this paper, we describe a method to quantify
the uncertainties of low-energy LXe responses using published calibration data,
followed by case studies to evaluate the impact of yield uncertainties on
${^8}$B searches and low-mass dark matter sensitivity in a typical ton-scale
LXe experiment. We conclude that naively omitting yield uncertainties leads to
overly optimistic limits by factor $\sim2$ for a 6 GeV/c$^2$ WIMP mass. Future
nuclear recoil light yield calibrations could allow experiments to recover this
sensitivity and also improve the accuracy of solar ${^8}$B flux measurements.
