[Tx Firefighter]

A limited slip rearend can absolutely do that. The most common cause is fluid issues. A clutch type of differential requires a specific type of fluid, but often folks just substitute the wrong fluid and it leads to issues like you're having. The first thing to do would be to change the fluid and refill it with the proper fluid that is specified as having limited slip additive. Then, take the truck to a parking lot somewhere and slowly drive it in multiple circles in both directions to cycle the differential with the new fluid. That often frees them up.