The Lunar Corporation is the subject of several old factories and mechs, usually found around the island of Hemica. The Lunar Corporation is only discussed once and the topic isn't revisited again. It's highly assumed that the show's creator, Hakima Futamosho, wanted to create a spin-off of M³ dealing with The Lunar Corporation, but nothing has ever been confirmed.
It is unknown as to when the Lunar Corporation was established, but it almost definitely preceded the Nova Corporation. Others may speculate that the two founders of the Lunar and Nova Corporation were in fact brothers. There is a common theory among fans that The Lunar Corporation is indeed an earlier, failed attempt at Cyblain enslavement of Earth.