Ultralow energy calibration of LUX detector using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Xe</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>127</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> electron capture

We report an absolute calibration of the ionization yields (${Q}_{y}$) 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 $180\text{ }\text{ }\mathrm{V}/\mathrm{cm}$. The data are obtained using low energy $^{127}\mathrm{Xe}$ electron capture decay events from the 95.0-day first run from LUX (WS2013) in search of weakly interacting massive particles. The sequence of gamma-ray and x-ray cascades associated with $^{127}\mathrm{I}$ deexcitations produces clearly identified two-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 in situ measurements that have been explored in liquid xenon.