It might be possible your limited slip rear axle needs some 1) friction modifier, 2)fluid replaced with friction modifier.
There has been a good deal of talk about this (if it is indeed your LS)...try a search on the limited slip topic and see what you find.
I decided NOT to go with LS when I ordered my 2000 for this reason. Other members posted that they were hearing 'noises' from the rear gears when making turns..etc.
2000 F-150 XLT, 4x2, 5.4L Supercab, Styleside, Black with silver two-tone, 3.55, class III towing package with heavy duty cooling package, 4 wheel disk ABS, overhead console, sliding rear window, keyless entry, dark graphite interior, in dash CD, Pendaliner bedliner, K&N air filter, rubberized undercoating, cabin filtration system, Bugflector II, 5W-30 Mobil 1, engine build 10/4/99