[Loser]

Sure L4 and L5 are great places to put stuff if you want to send it somewhere else on the cheap, but they're not such great places to work.

Microgravity is very inconvenient. Not only is it difficult to keep humans healthy in microgravity, but it's hard to work, to move things around (inertia and torque messing with you), and many machines must be built very differently to work without gravity.

The lower gravity on the moon would still be troublesome, certainly, but it would help.

Before someone brings up the spinning-wheel space station concept I'll point out that it is very difficult to do right. The problem is that as people move through the station, the station itself will move around in space. A great deal of fuel will be needed to keep it at it's intended location.

You might remember seeing pictures of American Astronauts running around the inside of Skylab, no? Yeah, they were knocking that like box all of the place while they did that, and Skylab was not properly fitted to keep it's orbit anyway.

Since an object near either the L4 or L5 positions will be gently pulled toward the actual specific Lagrange Points, you might be able to put a spinner up there and just let it go, depending on the attraction of Luna's Trojan points to keep your station where you want it. I don't think that's such a good idea, myself, and every damn thing in the station would have to hold real still when time comes for anything to dock with it.