Two problems related to transmission not go into gear have been reported for the 2001 Lexus RX300. The most recently reported issues are listed below.
While traveling at 25 mph the car stopped accelerating forward and seemed to not be in gear. As I pressed the gas pedal the engine revved up, but would not go forward. Car was taken to the dealer who stated even though the car only has 123k , you need to replace the transaxle. I confirmed that their was no maintenance required.
I was driving home from vacation and the car would not go into gear as I was driving on the highway. I pulled over on the shoulder to try to get it to go. It stalled for a while then kicked back into gear. I got off at the next exit and then the atf light came on. I put some transmission fluid in the car and slowly drove home. The car died in my driveway. I had to get the transmission replaced ($4,000).