First of all, what year is the car. There are some common problems on most models, which involves faulty climate control and radio displays (many of them were replaced under warranty). Our 1996 LS400 is not far from 100,000 miles, and it's had a few problems. The "front castor bars" have cracked no less than three times and were replaced all three times under warranty (the last one was claimed "courtesy warranty," but I know Lexus issued a TSB on it). Didn't affect the driveability of the car at all. Another problem was a cracked EGR tube at 65,000 miles, replaced under California Emissions Warranty. One "small" problem was the electric antenna motor, which died at 45,000 miles and cost $180 to fix. Best advice I can give is avoid the Lexus dealer like the plague, unless you enjoy getting taken for a ride. On the other hand, new shocks all around only cost $150 from the Lexus dealer! The interior hasn't aged as gracefully as I had expected it to (poorly worn leather, warped wood), but it's still a gorgeous car. The Tahara plant (where LS400s are built) is still one of Toyota's best for quality, and it shows. The car is without peer as a rock solid highway cruiser but still handles twisty mountain roads with astounding poise (will get you there as quickly as a comparable BMW 740i, just not quite as much fun). The car returns about 17 mpg in suburban driving, but once out on the highway, it never moves from 25 mpg, even with the cruise set at 90 mph and the A/C going. The car does everything effortlessly... including venturing up to the 149 mph governor.
