From your first post it sounds like you are planning on a regear at the same time - that will require a full gear setup.
We bought the Jeep and it has a small lift and 33 inch tires and was pretty gutless. Gearing appeared to be 3.55 and from what I read we needed to be 4.56. I ordered the 4.56 rear and matching front gearing from Extreme Terrain, but hadn't taken it apart at that point, so didn't know it was LSD. Someone had clearly been in there before as the carrier bearing caps were on wrong and now I know why. I suspect the lift kit was put on after the LSD or it would have been geared lower?
A friend and I are rebuilding it (he has done a few before) but now I'm not sure which way to go as I have all the parts to rebuild Open diff... except I now need a new carrier if I go that way. Rebuilding the LSD didn't look too bad but in one of the video's Andy White sent me, the guy changed the ring and just put the standard shims (one each side) either side on the carrier and made no mention of the pinion or setting up the backlash. Maybe I need to watch it again?