As far as the braking, have the fluid level and pads checked out first . Maybe there is air in the line. It may also be within your Hydraulic brake booster. This brake system actual controls line pressure and sometimes feels like a sponge. It could be faulty, and you might not have any warning lights on the dash, but it would be stored as a hard code in the ecm( not a code autozone can pull either). You are better off going to a toyota dealer (or someone who specializes in lexus) and have it checked out. After you have your tires checked and balanced (with a road force balance of course) and aligned and you still have a shimmy (I would say between 60-67 and again between 78-85) have your steering rack bushings checked out (as well as ball joints,tie rods and the whole front end). How many miles are on the car? Do you have any service history? This is why I say, bring it to someone knowledgeable to get it serviced up to date before you add rims and such.