FWIW, he lists it as fitting the '00-'05 LS, but that's quite clearly a kit for a 1st Gen LS (the 2nd Gen shifter surround is rectangular).
The picture on eBay only shows 1st gen parts. The parts that go on and around the shifter are immediately recognizable as 1st Gen parts; they will NOT fit a 2nd Gen LS as-is. I don't know about the rest of the dash/trim pieces, but the pieces that go on the center console are not universal.It looks like it has pieces for both gens. So you will get some extra pieces.