The feasibility of a Lunar LIGO (Laser Interferometer Gravitational-Wave Observatory) was introduced in 1986 as part of NASA’s planned return to the Moon by the end of the last century. That return to the Moon mission was cancelled, but is once again planned as Artemis in 2024. In this paper, the feasibility of such a Lunar LIGO as part of NASA’s return there will be discussed for that program. Details of the physics of the original Lunar LIGO proposal as a potential portion of future lunar base astronomy and astrophysics designs are presented. Results from NASA’s original planned return to the Moon to establish a gravitational wave observatory there are presented and discussed.