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I bought my '02 Z28 new and ran M1 5w30 in it for nearly 150k miles, always changing the oil according to the OLM. When I realized that SM oils had reduced levels of ZDDP (zinc-based antiwear additive), I began seeking out oils that have at least SL levels (1000ppm of Phosphorous). Since then, I have run M1 High Mileage 5w30, M1 0w40 European Formula, and Redline 5w30. I have steadily run the car in road course track days its entire life, and at 193k miles, the engine is still noise-free, makes good power, and burns about 1 quart of oil in 6000 miles.
I can recommend all of the above oils for the LS1, and there are some others that are on my list to try:
Castrol Syntec 0w30.
Pennzoil Ultra 5w30 (but not for track use due to low HTHS).
Valvoline MaxLife synthetic 5w30.
AMSoil Signature Series 5w30.
Or go back to M1 5w30 in the SN specification.
If you are not running your car on race tracks, the LS1 is easy on the oil. But if your are going on track, the LS1 can oxidize the oil if it is not equipped with an oil cooler. (Mine isn't, and it did oxidize the M1 0w40, which is a high-performance oil.)