Towing a Car Trailer

Don't go by what took place in the 70's. First, many laws have changed regarding trailer towing, since the 1970's. Also, the station wagons in the 1970's were much bigger and much heavier than you Lexus. Don't forget, your Lexus RX300, is essentially a re-bodied Camry.
The RX300 is the shortest, narrowest, lowest, and lightest entry, in it's class of car based SUV's.

What are you planning to put on the trailer, an A body? Street car, or racer?

You'll need to look at two capacities on your Lexus, Towing capacity, and tongue weight capacity.

The addition of a trans cooler might also be a good idea.
Today's car have operating temps of 195º whereas the old 1970's station wagon, operated at 165º to 180º.

Your Lexus will require a lot of help, stopping. While it has good breaks, adding the weight of a trailer and a car will tax your SUV's brakes, and that's not a good feeling.
Personally, I'd never even consider towing a car without trailer brakes.

Most "A" bodies can easily be town by a half ton puck up, the slightly longer wheel base of a pick up also improves the ride quality, over that of must SUV's with their shorter wheel base.