The sway bar bushings cause more of a knocking noise, at least in my experience and from what I read on this forum. The knocking happens when hitting even small bumps or holes, caused by the bushing being worn to a larger diameter and the bar banging around in there. I don't think the noise you describe fits the sway bar problem.
Let me add that the sway bar knocking noise problem is apparently very common on the LS as they age. I just changed my bushings with the help of this forum, and it not only eliminated the knocking sound, but the car handles much better in the twisties. It was not an easy job due to the tight spaces involved, but worth the effort. If you can spare $120-150 you can easily find a mechanic to do the job.