You can program the remote portion of your 1999, 2000, 2001, 2002, and 2003 Lexus RX300 yourself at home with this procedure:

**Key must be separately cut and (chip in key) programmed by dealer or locksmith to start the car… this procedure will only program the remote buttons on the key**
Driver’s door open, all other doors closed, key removed from ignition switch.
Within 5 seconds:
Insert and remove the key from the ignition switch twice.
Within 40 seconds:
Close and open driver’s door twice.
Insert and remove the key from the ignition switch.
Within 40 seconds:
Close and open driver’s door twice.
Insert the key into the ignition switch and close the driver’s door.
Switch ignition ON and OFF:
Once to program a key remote transmitter code whilst retaining the original codes.
Twice to program a key remote transmitter code whilst erasing the original codes.
Three times to check how many key remote transmitters are currently registered.
Five times to erase all registered codes.
Remove key from ignition switch.
System should now lock and unlock vehicle once, twice or five times depending which mode has been selected. One to four
times, slowly, to indicate number of remote transmitters registered.
Within 40 seconds:
Press and hold LOCK and UNLOCK buttons Fig. 1 or Fig. 2 simultaneously for 1.5 seconds.
Within 3 seconds:
Press and release LOCK or UNLOCK button Fig. 1 or Fig. 2 .
System should now lock and unlock vehicle. Once to confirm registration or twice to indicate registration has failed.
Within 40 seconds:
Repeat button procedure to program remaining key remote transmitters.
NOTE: To exit programming mode: Open driver’s door or insert ignition key.
NOTE: A maximum of 4 key remote transmitters can be programmed.