Two problems related to transmission not engage have been reported for the 2001 Lexus RX300. The most recently reported issues are listed below.
Driving on the freeway. Transmission disengages and fails to drive car. Automatic transmission failure. Serviced transmission at 63,200 miles. Many others have reported problems with this model year.
1) while driving on 101 freeway in los angeles on a 90 degree day the transmission would not engage. 2) the transmission failed and I was able to avoid a crash by exiting the freeway. 3) the auto dealer made a good will repair even though it was just out of warranty.