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.