An easy way to determine if your car has a LSD is to raise one rear wheel off the ground and with the transmission in neutral, spin the raised wheel with your hand. If it spins freely, you most likely have an open differential. If you feel resistance, you probably have a LSD.
Another test is to lift both rear wheels off the ground, put the transmission in gear, and turn one of the wheels by hand. If the one on the other side rotates in the opposite direction, you most likely have an open differential. If they rotate in the same direction, you most likely have a LSD.
With one wheel fixed (someone holding it in this case, could also be on the ground), either in neutral or in gear, it is very difficult to turn the other side at all, but it will turn given enough force.
See if you can try these.
Another "test" of LSD.