Selenostationairy seems to be impossible. It would be too close to earth to fly undisturbed. Orbiting the moon is hard because of the moon's uneven mass concentrations, the gravity is not as uniform as here on earth. An space-based LPS would be pretty hard to build out. Star trackers alongside GNSS would provide a better system for positioning.

However, building out a ground system using towers on the moon would work. With the low gravity of the moon and no wind, you could build pretty tall structures with beacons for positioning. You'd need line of sight so it would be costly to build out this system across the entire surface.

A 1km tall tower built every 58km would give you similar positioning as GPS (three intersecting circles). But also, the moon is not terribly interesting so the few long trips that would put you far from base wouldn't require instant positioning. A star tracker and an hour of watching GNSS would work just fine. If there ever was a significant population on the moon, they'd have the lunar equivalent of busses (traveling over marked paths) or light rail to get them in-between facilities.