I would either go with viper or compustar, your going to need a few extra parts (extra relays, and an immobilizer bypass), most importantly, you need to find somebody that is very familiar with the LS to do the install as there are a few unusual things about the LS that is different from most cars. and you always want to buy the remote start from the place that is doing the install for any warranty issues.
personally if I was starting over and putting a new system into my LS I would get a compustar brain (CM6200)
then you pick out which remotes you want to use with the system. all of compustar remotes will work, you just need to pick the one with the features you want such as size, range, and 1 or 2 way, personally I really like their 2way G9 remotes as they are pretty thin and small and have a great range (3000')
then you would need to get their bypass (the Blade) for the PATS
without looking it up, from memory I think you would need at least two extra relays for extra ignition circuits
factory alarm disarm, lock and unlock wires are all inside the drivers door (so are the wires if you want to be able to roll up or down the windows from the remote if your feeling spicy)
you dont need a relay for trunk pop, but you do need one for popping the fuel door open if you would like to do that from the remote.
other nice options:
you can get the EZGO add on if you want the doors to unlock automatically when you get close to the car
you can get the Drone add on if you would like to be able to start (or lock or unlock) the car using your smartphone with unlimited range.
