Gen 1 or 2? If it was a Gen 2, I'd agree on throttle lag (that's why I flashed my PCM).
Other than that, the most common problems on the Gen1/2 LSes are :
1) COPs (oil gets in, shorts them out. Ford covers them up to 100k)
2) DCCV going out
3) Plastic cooling parts cracking and system unable to hold proper pressure
4) Window regulator breaking
They're also a little touchy if the battery is low on charge, but that's about it.
Funny to see this thread - I just got rid of my '06 LS for these reasons. Had it for 5 years - bought with 30K miles and traded with 75K.
1) - Went through 2x sets of COPs. No oil leaking, it was due to the coils breaking down internally from heat. Lets put a cover over them, and then cover the cover with sound insulation.
2) - Yep replaced the DCCV last year
3) - Had to replace the T-stat housing last month
4) - No window problems.
Don't forget about the servo bore issue on the transmission that fails at around 75K miles. Or the drive-by-wire throttle ETC failsafe mode caused by COPs, or TPS, or failed throttle body. Or the genius hydraulic fan on the Gen1s.
The LS was easily the biggest money pit car I have ever owned! It was exciting to see a car that wasn't a blatent Taurus/Sable/Continental or Navigator/Expedition. It is a GREAT looking car, but I think they half-baked the Jag/Ford combo. After the LS, and my '12 Focus with the myriad of problems it has with the MFT and transmission. And being presented with a paper that says a grinding transmission is "normal", I have lost any/all trust in Ford.