First thing you will need is a LOT of patience and some free time
"Mesh is fine on all of them, but the lips are all in some degree of wear."
-Exact same as mine so I left that alone.
"Do the tires have to come off the rims to do the work?"
-I suppose you could keep them on although it will of course be easier without them mounted.
"Is it possible to only do work on the lips and leave the mesh untouched? That seems unlikely, but would be ideal."
-It is very possible and I will explain how I did so. Keep in mind that it's not going to be "perfect" and there will be some rough spots but that all depends on how well you seal the surface you want to keep in tact.
First thing I did was thoroughly clean the spokes/mesh (very important step since the tape will need a CLEAN surface to adhere to), don't worry so much about the lip since that will be stripped.
Buy a good quality automotive masking tape like the blue 3M type in both the 1" and 2" sizes. Starting with the 1" masking tape, start taping over the outer layer of the painted surface (i used the 1" first because it's easier to manipulate). This is what I would consider to be the most important process because as I stated earlier if the tape isn't completely covering the surface then your results may vary. Next, overlap the 1" tape with the 2" tape and when all that is done for added measure you can do another layer. Now you'll have what looks to be like a blue ring surrounding the outermost area of the spokes and just for safety you may want to cover the inner section. You could wast more tape but that stuff is expensive so what I did was be resourceful and use a plastic bag like the ones your groceries are placed in at the shopping center, just tape that to the "blue ring" to completely cover the exposed surface.
Now you can start to remove the clear coating from the lip. Buy an aircraft paint stripper in a container that can be brushed on. I found the spray on stuff to be more expensive and you will use more than one can so just buy the bigger container. Follow the directions on the container and once done you can proceed.
If you want a polished billet look:
Buy an assorted pack of Wet or Dry 3M sandpaper and start sanding the machining lines off, I wouldn't use anything too aggressive (I think I started with 220). Work your way down on the coarseness till you get a polishable surface. Use water to keep the paper from getting clogged up and take your time. This may seem like a lot of work at the time but when it's all said and done you will be happy!
If you just want a clean untarnished surface:
Use whatever cleaner/polish of your choice, and scrub away. Simple enough.
If you're not going to "seal" the surface with a clear coat or whatever keep in mind that you will need to keep the wheels clean since aluminum oxidizes very easily. Mine are left uncoated since I prefer to polish mine. I will show pictures as soon as I find/make some. Hope this helps