Good ol' Pektel put a Mustang LSD on his LS...and frankly I'd follow his advice if it came down to it :-D
Yep. From an 05 Mustang GT. I reused the ring gear and pinion, so obviously I stuck with 3.31's. Don't know if you have 3.58's in your's, but that's the best gearing you are going to get without swapping the entire pumpkin, fabbing brackets, and custom drive shaft as previously stated. 3.58's were found in all gen 2's and some gen 1's.
Shim kit for the 8.8 works for our 8.0. I had to buy one to find out.
Also buy new ring gear bolts. They see a lot of stress.
New axle seals, diff bearings too. I didn't buy new caps, don't know if you'll need to.
I bought motorcraft 80/90 and the friction modifier additive.
Pattern paint. Hopefully you have a dial indicator.
Other than the standard mechanic's tools, that should be about it for parts needed. Oh, let me know if you need torque specs.
Don't know how messed up it is in there though. May need new ring gear/pinion (which by how hammered you make it sound, there are almost positively some chipped/broken teeth)