One problem related to transmission not go into gear has been reported for the 2002 Lexus RX300. The most recently reported issues are listed below.
The transmission totally failed. Vehicle would not move in any gear. Rpms pegged out at 6k. Had the vehicle towed to northtown Lexus in amherst, NY. They agreed that the transmission was totally shot and would cost approximately $5,500 to replace, just for the part. I subsequently had the vehicle towed to continental transmission in buffalo, NY, where it was rebuilt for $3,100. I understand from posts at the Lexus owners club of USA that Rx300 transmissions are prone to failure as they were not designed for the added stresses imposed by and SUV.