First thing you do is push and pull every switch & button you can find, and i will tell you there are lots of em.
Give the car a thorough looking over, and under, in the wheel wells, under the hood, remove the boot spare wheel cover and have a good look around there, whilst you are there, look either side of the boot, satnav on the right, fuse box on the left, check for rust, fluid or anything that looks out of place.
Test drive it, does it pull to any side, gear changes should be smooth and almost not noticable, steering should be smooth and precise, they do handle quite well for a yacht with wheels, does it pull under braking, any rattles or knocking.
If you can, take another lexus owner along with you for a second set of eyes.