We utilize measurements of electron plasma frequency oscillations made by the two-probe Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun mission to investigate the charged particle density in the lunar environment as the Moon passes through the Earth's geomagnetic tail. We find that the Moon possesses a tenuous ionosphere with an average density of ~0.1-0.3 cm-3, present at least 50% of the time in the geomagnetic tail, primarily confined to within a few thousand kilometers of the dayside of the Moon. The day-night asymmetry and dawn-dusk symmetry of the observed plasma suggests that photoionization of a neutral exosphere with dawn-dusk symmetry produces the majority of the lunar-derived plasma. The lunar plasma density commonly exceeds the ambient plasma density in the tail, allowing the presence of the lunar ionosphere to appreciably perturb the local plasma environment.