the type of LSD doesn't effect the oil it takes, all LSDs just need a friction modifier to work. if your car has a LSD it may be marked on the differential with these letters or check the build sheet if you have it, alternatively get one tyre on grass and tyre on road and try accelerating hard, if the grass tyre spins but the road tyre does not the you dont have a LSD. alternatively jack up the rear wheels together and try rotating the tyre by hand in one direction and watch the other tyre, if they both rotate in same directions then you have a LSD, if they rotate in opposite directions then you dont
most probably you wont have it.