If I were to do something like that in the States I'd try to do as much after-market as possible, as the Lexus dealer pricing on OEM parts is very high. If I had a sound running LS400, I'd leave the engine untouched.
Breathing better is a basic of some extra performance so I'd look into intake and exhaust. I don't know if they make it but I'd look into a HKS or Tanabe cat-back exhaust, possibly even headers and cats. Intake-wise, K&N element would be a good start. If they made a carbon-fiber air-box that does away with the intake baffle would rock. I'd check Carbonio first but I think they mostly do Euro-cars.
Suspension is geared for luxury in the LS and I'd stiffen it up with some quality shock and springs. H&R springs makes some great springs that give better control without a dropped/slammed look. I think they have a series that's just 25-30% stiffer than stock but still offers much better control. I follow their recommendation as to which shocks to apply. Tokico has some adjustables but Bilstein are great as well.
When I need new brakes I'd replace with Brembo rotors and some high friction pads. Factory calipers should suffice, probably just get some rebuilds.
Wheels and tires are the final point of making an impression and expression, on the road and for the look of the car, respectively. I'd choose wisely. +1 maybe +2, just not overstated, as that's the best way to make a car look trashy. Mesh BBS with a bright or black lip might complete it for me. As for tires, I'm partial to Pirelli, they're cheap and grip well.
That's pretty much what I'd do.
"Racing improves the breed" ~Sochiro Honda