"Lunar gravity" refers to the force of gravity on the surface of the moon. It is the pull that the moon exerts on objects, which is weaker than the force of gravity on Earth. Full definition
The origin of the waves is basically similar to that of oceanic tides caused by the pull of lunar gravity. (britannica.com)
This is because the motion of the satellite is influenced by lunar gravity. (sciencedaily.com)
The change in gravity caused by the lunar deformation due to the tidal force is extremely small, but when the change in location of the orbiter can be determined precisely enough, it is possible to accurately detect the change in lunar gravity caused by the deformation due to the tidal force. (sciencedaily.com)