  Dual-phase xenon time projection chamber (TPC) detectors have demonstrated
superior search sensitivities to dark matter over a wide range of particle
masses. To extend their sensitivity to include low-mass dark matter
interactions, it is critical to characterize both the light and charge
responses of liquid xenon to sub-keV nuclear recoils. In this work, we report a
new nuclear recoil calibration in the LUX detector $\textit{in situ}$ using
neutron events from a pulsed Adelphi Deuterium-Deuterium neutron generator. We
demonstrate direct measurements of light and charge yields down to 0.45 keV
(1.4 scintillation photons) and 0.27 keV (1.3 ionization electrons),
respectively, approaching the physical limit of liquid xenon detectors. We
discuss the implication of these new measurements on the physics reach of
dual-phase xenon TPCs for nuclear-recoil-based low-mass dark matter detection.
