Little late to the party, but maybe this will help somebody else - looks like the OP is well down the road.
Every LS block I've ever seen has a laser-etched VIN on the machined surface of the deck on the back of the motor on the driver's side - there's no need to know the VIN on the chassis it came out of.
The deck has a 'lip' that the cylinder head does not cover, and that's where you'll find it. When I'm junkyard hunting motors, I usually take a little steel wool with me to rub the deck to reveal the VIN.
Per Jwebb, the 8th place of the VIN is the engine.
There's a pretty good rundown of all the LS variants here-
https://en.wikipedia.org/wiki/Genera...l-block_engine