I'd change the oil with whatever the cheapest stuff you can find is, add a hearty dose of seafoam, and run it hard for a couple hundred miles and change the oil again. Cheap investment and might clear it up.
Should be crazy easy. I helped swap an early LS1 into a '67 Camaro in 2004. It was a breeze back then, should be even easier now. LS1Tech.com, as mentioned, is a great resource.
Mine. I'm half-heartedly trying to sell it. '67 Impala. 396/Th400/3.73 geared 12 bolt. 100k mile original car. Motor should be in the 450hp range... car turns easy mid 13s at 104-106 on 225 Goodyear Eagles. Sticky tires, tuning, and a looser converter would maybe see a 12.99.