We report an absolute calibration of the ionization yields($\textit{Q$_y$})$ and fluctuations for electronic recoil events in liquid xenon at discrete energies between 186 eV and 33.2 keV. The average electric field applied across the liquid xenon target is 180 V/cm. The data are obtained using low energy $^{127}$Xe electron capture decay events from the 95.0-day first run from LUX (WS2013) in search of Weakly Interacting Massive Particles (WIMPs). The sequence of gamma-ray and X-ray cascades associated with $^{127}$I de-excitations produces clearly identified 2-vertex events in the LUX detector. We observe the K- (binding energy, 33.2 keV), L- (5.2 keV), M- (1.1 keV), and N- (186 eV) shell cascade events and verify that the relative ratio of observed events for each shell agrees with calculations. The N-shell cascade analysis includes single extracted electron (SE) events and represents the lowest-energy electronic recoil $\textit{in situ}$ measurements that have been explored in liquid xenon.