My Lexus Gs430 vibrates up and down when I only reverse at low speed. It doesn't happen when I drive.

 

Reverse faster.

 

Do you mean the whole car moves up and down?

 

Yeah, my 430 does a little shimmer/shake when I slowly back up too - but usually just on hot days. It's been doing that since I took ownership of it 15 years ago. I haven't done anything about it.

 

Transmission mount/engine mounts, most likely. Reverse gears are cut differently than the rest of your gears, so a lot of the time, the car will shake differently or more in reverse, making it more noticeable. Same reason the steering wheel is dead still in park, but might have more vibrations in drive. As long as it's not accompanied by a rough idle, you should be fine.
If it's been 15 years and that's the only issue to do with shaking/rattling, you're doing pretty good.