The LS does have electric power steering. Only the SS had hydraulic steering. And it does have to go to the dealer for a steering diagnostic and a possible intermediate shaft. And GM is aware of this problem. Even if your car is out of warranty - stand there a scream until they give you warranty. Ask for the number of the NHTSA if they don't give you satisfaction. GM has gone to great lengths to mask the fact that this steering system has design flaws and if you embarrass them and yourself enough they will honour a warranty claim just to shut you up. Stand your ground right in the middle of the service area and don't let them shuffle you off into the service managers office.
If it doesn't have a pump then it doesn't have power steering, could be the rack is seizing/damaged. If it does have power steering, check the belt isnt slack or missing.
