question?
 

how do i check if new/used rear end in car has LSD, and how do i check if old rear end out of the car has LSD?

There will be a tag attached with a bolt near the top of the diff on the LSD. With the LSD in the car, go find a spot where you can get one tire on grass or gravel and one tire on pavement, now floor it. An LSD equipped car will take off while the non=LSD car will spin the tire on the gravel or grass. If you don't like that method, jack both rear wheels and spin one wheel. If the other tire spins in the SAME direction then you have LSD. I'm not sure how accurate this method is as some ppl have said this doesn't apply to all diffs.