We present high-precision theoretical predictions for the electron energy spectra for the ground-state to ground-state β decays of 214Pb, 212Pb, and 85Kr most relevant to the background of liquid xenon dark matter detectors. The effects of nuclear structure on the spectral shapes are taken into account using large-scale shell-model calculations. Final spectra also include atomic screening and exchange effects. The impact of nuclear structure effects on the 214Pb and 212Pb spectra below ≈100 keV, pertinent for several searches for new physics, are found to be comparatively larger than those from the atomic effects alone. We find that the full calculation for 214Pb (212Pb) predicts 15.0%–23.2% (12.1%–19.0%) less event rate in a 1–15 keV energy region of interest compared to the spectrum calculated as an allowed transition when using values of the weak axial vector coupling in the range gA=0.7–1.0. The discrepancy highlights the importance of both a proper theoretical treatment and the need for direct measurements of these spectra for a thorough understanding of β decay backgrounds in future experiments.