If it's from an US '81 280Z(X) chances of it being an LSD are very close to ZERO, unless someone put one in it, 'cause the factory did not.
The way to tell is to jack up the rear of the car, make sure it is out of gear and turn one wheel. If it is an LSD the opposite wheel will turn the same direction. If the other wheel does not turn or turns in the opposite direction, you got yourself a peg-leg (non LSD, Open Diff.).