Hmmm, does it gring when you are moving slowly in reverse? Is it really a grinding noise or is it more like the tires are rubbing and the car kind of jerks a little?
Reason I ask is maybe our LS have limited slip differentials and Maybe yours is "grabby" and could use some limited slip additive.
I do not know if the LS has limited slip, many rear drive perfomance axles are limited slip so I would guess better than 50/50 odds of us having it.
The test for a limited slip needing additive is when in slow speed tight turns, especially in reverse, the differential will "chatter", quick little grabby feel of the car like the brakes cutting in and out or the tires grabbing on the fender.
If this is what is happening you might try a tube of limited slip additive available at most autoparts stores. COmes in a big toothpate tube and costs soemthing like $5? Usually use one tube to cure the chatter.
First we need to findout if the LS has limited slip.
BUT if it is a metallic grinding noise, then you are looking at potentially an expensive problem. If it is the brakes, you need to pull the pads right now or at least take a good look at the rotors, both sides. Inspection is easy and free if you do it yourself. Pull each wheel and take a strong light and inspect the rotors.
If there are grooves big enough to easily catch your finger nail, then you probably had a pad wear out and got metal to metal contact. You will need to have the rotor turned if you are lucky(about $20), or you will need new rotors(maybe $100 plus or minus a lot).
A mickey mouse temporary fix would be to use new pads, but realizing the brakes are questionable and they won't wear as long.
Good Luck,
Jim Henderson