Can a transmission get stuck?
As in stuck in Park? Yes it can. IF this is the case, It sounds like your shift interlock isn't releasing. There should be a shift interlock override to release the shifter if you get stuck somewhere and can't get it out of park. The override may be hidden under a cover plate on the steering column or shifter console, and you may have to use a pen, ignition key or small screwdriver to access it. Your owner's manual may tell you where the override is hidden.
Really need more information on what you mean by "stuck". Will the lever move? Are you Uphill or Downhill? Against a curb?
Parked in the driveway
If I push the overide button it moves. but I dont want to have to keep doing that.
Then the lockout is not getting the signal when you step on the brake pedal, could be the solenoid or a wiring failure from the brake switch to the release solenoid.
Looking for a Used RX 300 in your area?
CarGurus has 1,061 nationwide RX 300 listings starting at $2,363.
Search Lexus RX 300 Questions
Lexus RX 300 Experts