Be aware that there is a very limited market for the LS. They have a terrible reputation and it takes the right buyer to pay anything over trade in value for one. An 01 V8 to the right buyer private party maybe $4,000.00 on a great day but be prepared for offers in the $2,500.00 range. If you end up trying to trade it in expect $1,000 as an offer.
Last year alone a boatload of low mileage second gens came on the market for whatever reason. I was lucky enough to grab three at auction for next to nothing. 05 LS8 with 21k miles and fully loaded for $4,000.00, 05 LS8 with 18k miles and three options shy of fully loaded for $4,100.00, and 06 LS8 with 23k miles base model for $4,500.00. All three of those cars are the much more desirable second generation model and no one but myself bid on them at auction.
I also of a dealer lot spent $10,000.00 for an 06 LS8 with 10k miles on it before buying the other three at auction. I tried to sell that 06 for over 6 months after I got tired of it. I didnt have single buyer for anywhere near the 10k I payed for it. The highest offer I received was for $7,000.00.
I ended up taking all four LS8s to the track and racked up a couple hundred miles each where they never came off the rev limiter and then dumped all four at auction for $10,000.00. Best of luck to you and hope you can fetch a decent price but unless your market is vastly different than my local market I wouldn't expect to get much more than a very low trade in value.