The Large Underground Xenon (LUX) experiment is a 250 kg active mass dual-phase time-projection chamber (TPC) operating at the 4850 ft level of the Sanford Underground Research Facility in Lead, SD. Various sources, including ^{127}Xe, D-D neutrons, ^{83}mKr, Tritium, and AmBe neutrons are used to perform calibrations of detector responses to electron recoils (ER) and nuclear recoils (NR). I will present an ultra-low energy calibration of ER using an intrinsic ^{127}Xe source and of NR using a short pulsed D-D neutron generator. Radioactive isotope ^{127}Xe is formed in the LUX LXe volume due to cosmogenic activation before the detector was moved one mile underground. A measurement in the early stage of the LUX WS2013 science run unveils ~0.9 million ^{127}Xe atoms in the LUX LXe volume, which provides an ideal source for low energy calibrations. ^{127}Xe decay is a form of electron capture in which a high energy gamma (> 200 keV) is emitted, followed by an associated low energy X-ray cascade over the energy range of 190 eV to 33.2 keV. The relatively long mean free path (mfp) of the gamma-ray (> 0.9 cm) allows the EC decay to produce clearly identified 2-vertex events in the LUX detector. We observe the K (33.2 keV), L (5.2 keV), M (1.1 keV), and N (190 eV) shell cascade events and verify the relative ratio of observed events for each shell. We extract the means and sigmas of the charge signal yields associated with the K, L, M, and N shell events. 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. A short pulsed D-D neutron NR calibration was performed in situ in the LUX detector in June 2016 after the completion of the LUX WS2013-16 science run. The calibration incorporates a pulsing technique with narrow pulses (20 us / 250 Hz). We have measured, with low systematics, the absolute rates of NR events with ionization signals down to 2 extracted electrons and zero, one or greater detected scintillation photons. A calibration measurement with absolute event rates of charge-only S2 events for the first time in a Xe TPC provides an important probe for ultra-low energy measurements of LXe Qy. This technique provides direct measurements of scintillation and charge yields down to (Ly) 0.45 keVnr and (Qy) 0.27 keVnr, respectively. New calibration results on ultra-low energy nuclear recoil yields are crucial to determine physics search sensitivities for large mass LXe TPCs (LZ experiment) for low mass WIMPs (< 10 GeV) and for coherent neutrino scattering (e.g. ^8B solar neutrino).