Oh here is another way to test lsd... lift one rear tire up. Put the tranny or the tcase in NEUTRAL (not park or in gear) The driveshaft has to be free to spin from the engine.
Try to turn the lifted up tire. If you can turn it and the driveshaft turns, you have an open one. If the lifted tire will not turn nor the driveshaft wont turn either, you have LSD.
If you have LSD you will pop a blood vessel before the lifted tire spins.
This is the safest way i can think of testing it.