Never replaced one but here's an easy way to test it...
Drive to a parking lot/deserted road/[insert place to avoid cops here], and just have a little fun powerbraking.
How to powerbrake if ya don't know:
put your left foot on the brake and right on the gas, hold the brake down hard at first then press the gas enough to hit ~2.5k RPM, just release the brake enough to get the back to break loose and creep forward while spinning your tires.
Be careful not to waste to much tire, and I know it sounds primitive, but if you leave two even marks on the ground your LSD is OK. And it is an easy way to be sure your LSD works.