So it makes the noise when the car is in gear and moving. Is it the same in all gears, and does it change when you turn? It may be something as simple as a throwout bearing or pilot bearing.

Oh, wait, nevermind.. If it's an LSD problem, it should make that noise anytime the car moves, regardless of whether the car is in gear or not. The LSD can't be disengaged from the wheels; it's on the output side of the transmission. It will also make a different amount of noise (more or less, depending) during a turn because there will be a speed difference between the two output shafts.

So I think it's probably not the LSD.