Easy way: The axle will hopefully still have a readable tag on it attached to one of the cover bolts, I guess hopefully it still has one at all. It'll say something like 3L55 or 3L73 etc. it'll be a limited slip. The key part being the "L", otherwise it'll just be a blank space for an open carrier.
Slightly more involved: is it a new (to you) truck? I like giving them a full round of fluid changes regardless, a bottle of oil is way cheaper than axle parts. So it'd be a good time to pop the diff cover, let it drain and look around. There are 2 types of L/S, torsen (fairly rare) and the clutch type (very common).
The clutch type will have the regular spider gears showing but also have some tabs poking out off to either side of them. Regular carriers will not have them. The Torsen should be a completely enclosed carrier (IIRC), and you should be quite happy as thats the really good one. Not that the clutch type is necessarily bad.
Jacking up the rear end should still work, if it's still in spec. Worn out clutch L/S's are pretty much act like open differentials.