Don't know on the LS for sure but I know chebbies and I think I read some of the LS have problems with the plastic rollers grinding themselves up and going off track. The regulator is something the dealers love to replace because it usually fixes window problems and they make big bucks doing it.
But the rollers are often all that is wrong, especially if the window is off track.
If you are decent with tools(ie you know how to remove the door panel) you can at least check for yourself to see if the rollers are chewed up. You remove the door panel and look at the rollers in their tracks. If the rollers are broken or chewed up or out of the track you have found the problem.
The parts at least for my old chebby are about $1 each, usually takes two rollers. Most people grind a slot in the track to slide the new roller in and pop it into place. Some just use pliers to bend the channel open. Do this away from where the roller will travel otherwise it will pop out of the track at the cut or bend.
The one gotcha is that the metal edges in the door are often very sharp and will cut you to ribbons if you are careless.
The job takes maybe half an hour to an hour depending on how many times you have to stop to mop up the blood.
Good Luck,
Jim Henderson