One problem related to transmission solenoid has been reported for the 2001 Lexus RX300. The most recently reported issues are listed below.
Vehicle has been well maintained with regular oil changes and transmission flush. However, on 06/22/2015, under normal driving conditions in my 7 miles commute, the vehicle failed to accelerate after coming to a stop. The rpm/engine revved up, but vehicle did not move much (could not shift gears). Pulled to the sideway and called for help. Took it to local mechanic, and diagnosed with code p0770 (solenoid shifter e failure). Mechanic says new transmission is needed ($5k plus). Checking online, this seems to be a very common occurrence for this vehicle and probably model year. Toyota has to be aware of this major defect, and has probably intentionally said silent. I wish Toyota could be taken to task on this problem as it is wrecking family finances!.