Welcome to the board!
In my experience, the failure mode for an LSD is excessive noise when turning...but more of a grinding or clucking sound. In either case, it absolutely couldn't hurt for you to drain the oil out and put in a fresh fill of diff lube (check your owner's manual for the exact weight), and visit your Nissan dealer for some LSD additive. If you bought the vehicle used, it's possible the differential was drained and not filled with the additive. If you bought it new, perhaps enough oil has leaked out to cause a noise, or perhaps the additive has expired. In either case, it won't cost more than 20 bucks (or so) to do a drain/refill on it, and it might solve the problem. If not, you may need to have a mechanic take a closer look at it.