My Camaro, which other posters here are probably tired of hearing about, has a long, storied history. I bought it new in 2002, and immediately put it to work doing autocrosses and track days during the summer and being my daily driver in the winter. Over the years, it has accumulated about 100 days on tracks from Calabogie, Ontario, to Buttonwillow, California. On track, it has run in conditions from 45 degrees and rainy to 107 under the blazing sun. In the winter it gets two cold-starts a day in temperatures down to -15.
And all through the first 152k miles, I put nothing in it but M1 5w30 and changed oil when the Oil Life Monitor told me. Then at 152k, I switched to M1 5w30 HM and noticed that oil consumption decreased from about 1/2-qt in 4000 miles, to 1/2-qt in 5000 miles. Then I switched to Redline at 160k miles. I didn't really have a reason to switch, I just wanted to see how it would run in my engine. On Redline, the consumption has dropped to about 1/2-qt over the change interval of 8500 miles. On the last oil change at 169k, I put in a mix of RL 5w20/5w30/0w30, basically just using up stray quarts.
So I state with confidence that an LS1 does not need a 40-weight oil under any circumstance. Oils that I would feel good about running in it are:
M1 0w30, 5w30, 5w30 HM, 10w30 HM
RL 0w30, 5w30, 5w20
AMSOil 0w30 Signature Series
GC 0w30
PP or PU 5w30
But really, any name brand 5w30 that is at least semi-synthetic will be OK.