The Lunar Fortress is a crystal palace located on the Moon.
The fortress has since become her lair, though she can only visit it when she has the moon crystal or finds other ways to reach the moon, like hitching a ride in PJ Masks Headquarters, or being towed in a moon bubble by Motsuki.
The fortress has, among other things, a throne for Luna Girl, and various statues of her. In "Moon Madness", she upgraded the fortress with a mega magnet, capable of generating a moon beam that could pull objects from Earth to the moon. At the end of the episode, though, the mega magnet was destroyed by the PJ Masks.