tl;dr: Start with a terrestrial GNSS constellation at a medium lunar orbit, but add more satellites in polar orbits to make sure you can still get a good fix sitting at the bottom of a crater at one of the poles.
The main spacecraft for all of Earth's GNSS systems are in medium Earth orbit (MEO) and this allows for enough members of a relatively small constellation to be visible and well above the horizon at any one time for most places on Earth, and for them to move fairly slowly across the sky.
The Moon has no atmosphere so no problem with variable water along the paths and ionospheric disturbances distorting the signal times from different satellites, but there are still horizon-blocking craters that folks will be driving in between and down into, so I think the model terrestrial GNSS constellations are workable, though you may need some more and put them in polar orbits.
The answer to What (actually) makes Iridium "the world's only truly global mobile satellite communications company"? is that they are in polar orbits, not 55° and 56° like terrestrial GNSS. The answer to Why do orbits in the Iridium constellation have an inclination of 86.4°? is that anything other than 90° is used to avoid collision, and 86.4° is used specifically to make the equatorial passes parallel to the meridian (by matching Earth's rotational speed at crossing).
Is there a way to establish a Lunar satellite positioning system that could be operational for decades? Would the satellites need to carry additional fuel to periodically adjust and "re-stabilize" their orbits?
Yes! and Yes!
In MEO the GNSS satellites really need very little stationkeeping. The higher order lumpiness of Earth's gravitational field is very weak out there, perturbations still come from the Sun's and Moon's gravity and from solar pressure. The answer there is that stationkeeping is occasional, perhaps yearly, just to keep them all spaced in a nice uniformly-spaced and easily predictable pattern for old, legacy receivers. A modern GNSS system (for Earth or Moon) could be designed with smarter and higher-quality receivers in mind.
The Moon gas lunar mascons which are extreme lumpiness in its gravitational field compared to Earth's but these are quite localized phenomena near the lunar surface and therefore reflected by very high order terms in the lunar gravy field's spatial harmonics. In other words, they would not be an issue in medium lunar orbit far from the surface.
Now, the size and frequency of the stationkeeping maneuvers might indeed be larger. If the Moon is a small effect on a terrestrial medium orbit, then the Earth will be an 81 x times small effect on a lunar medium orbit.
This perturbation might be so predictable, ephemerizable and distributable among the satellites that this doesn't turn out to be a huge problem.
And since all-electric propulsion satellites are becoming increasingly the standard way to make communications satellites from Starlink in LEO all the way to large commercial and government satellites in GEO, I think the higher stationkeeping delta-v per year in lunar medium orbit will not be a challenge for a modern satellite constellation.
From All About Circuits' The Limits of Satellite Navigation: GPS Challenges in the Arctic
Figure 1. Skyplots of GPS satellite constellation for Copenhagen at 56° N (left) and for Longyearbyen at 78° N (right). Plots generated with Leica Geo Office software.
