what you're describing is just a trait of both wheels either having traction or both wheels not having traction. if both have the same amount of some traction, you will get the same effect too. say they are slipping, but gripping about 50%. as long as they are doing the same on both sides, it will act as if the diff is locked becuase both right and left sides will be getting the same amount of power. if one side gets a little more traction and the other side slips a little more, and you gun it, you will know if you have an LSD because it will keep doing the equal slipping thing on both sides. but yeah, the only way to test it is to lift the rear axle up, both tires, in neutral, with no parking brake, chocked front tires and spin one rear tire. if the other rear tire spins the same way, you have it, if it don't, you don't. or, you could take the diff out and look inside. if you have side and spider gears, you don't have an LSD, if you have a big shiny cylinder, you do.