The Loric Museum of Exploration was a museum built by the Loric on Lorien. It was a museum that was completely dedicated to the evolution of space travel.
One specific artefact was Raylan's Ship, an old fuel powered ship that was allegedly used by his Grandfather, an Elder at the time, during The Secret Wars. During his obsession with the wars, Raylan spent a large amount of money restoring it but was later convinced, by his wife Erina, to donate it to the museum.
During the Mogadorian Invasion of Lorien, Raylan knew that his restored ship could allow his family to escape the planet but agreed to stay and fight, allowing Crayton to take his daughter Ella and his menagerie of Chimæra to the ship to escape.
Number Four later sees visions of three Cêpan, and the Chimæra being loaded into Raylan's ship. Just as the ship is about to take off he see's another man, presumably Crayton, enter the museum with a bundle, Ella.
It is unclear what happened with the museum, but it is likely that it was destroyed, along wth the rest of the existing buildings on Lorien.