I have 1998 LS400 I'm still having issues with the " No Reverse " problem. It reserves when its warmed. I replaced the Trans fluid with toyota ATF fluid and the Trans Filter change. The problem persist tho. When I had it in reverse I raved it a little and the engine light and check VSC light came on. Ran the codes at autozone came up as a speed sensor, Will a faulty speed sensor cause the Reverse problem.

 

Could be a faulty transmission solenoid. The solenoids are accessible by taking the transmission pan off. I believe there's only 1 solenoid under there that controls the reverse functionality.