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Synthetic 75W-90 is REQUIRED. They come factory with synthetic, make sure you get one that comes with the limited slip additive (like RP or Amsoil) just in case.
You DO NOT need limited slip additive unless you have added one with clutches yourself. The factory locker/limited slip is all hard parts with no clutches (and famous for self destructing).
The G80 locker does have clutches and the GM fluid has the additive in it.