if you get an extended warranty, you should be okay. I say this for a couple reasons...
The LS has a few trouble spots as KD00LS said, but I'll add to that:
window regulators (controls the windows going up and down) (first Gen)
Ball joints (suspension) (mostly first Gen)
Hydraulic cooling fan (engine-cooling) (First Gen)
Valve cover gaskets (engine) (00-mid 03)
PVC Hose on V6 (engine) (all years)
And the things KD00LS said:
Solenoid packing has been replaced (transmission) (first Gen)
Valve body has been replaced (transmission) (first Gen)
Coils (engine-ignition) (all years, but accelerated by valve cover gasket problems)
Tie rod (steering-suspension) (all years)
These are not areas you WILL have a problem with, they are just areas that have what most of us would say a more frequent occurrence of problems across the board than most other vehicles. There are a lot of owners who never have a lick of trouble, then there are a few that have all of them. Most of us experience one or two issues. It is to be noted that second generation cars have fewer of these problems, but some are shared. First generation cars are 00-02, second are 03-06.
If ultimate reliability is your goal, Honda, Nissan or Toyota would be your best bet. But that isn't to say the LS is horrible, just be aware that it takes a bit of maintenance.