The LS has a really long serpentine belt and it goes thru lot of pulleys. My GUESS is that this is just the nature of the beast and some will squeek no matter what.
Experience with other cars is that you can do some things to help.
A new belt often does the trick. Another car group had good experience, including me with the Good Year Gatorback belts. Don't know if there is one for the LS. They are a bit more expensive but they don't squeek. If anything they have kind of a supercharger whine to them but very faint.
Clean pulleys and belt. I sometimes will clean all the pulleys with alcohol or brake cleaner. DO NOT use anything that has oil in it like petroleum solvents. DO NOT use belt dressing, it seems these really gum up serpentine belts.
Sometimes I rough up the pulley surfaces with some coarse sand paper.
You can sometimes clean the belt enough to stop squeeking. Use rubbing alcohol or similar. I think Brake Cleaner is not good on rubber so I don't use that. DO NOT use petroleum solvent. If the belt is shiney, ie glazed, then you are probably doomed and need a new one.
Sometimes it isn't the belt, it is a bearing in one of the pulleys. This can get expensive since Ford seems to like to use non standard bearings so you have to buy a whole assembly including mounting arm sometimes. This happens even on lowly common as dirt Tauruses, lord knows how special our LS pulleys might be.
Just my experiences with other cars, my LS doesn't squeek so far.
Jim Henderson