Hello Dave,
Well, that's not quite so IIRC. As George said the transmit can be generated by the micro controller in a transmitter. All you need to do is generate pulses of 8.3usec repetition rate and turn them on and off as per the code you want to send. That is very easy to do with a uC and I believe that's how the RR501 works. This pulse rate is controlled by the crystal or resonator that operates the master clock of the uC. This is going to be very accurate.
True, the signal then has to pass the LC circuit. It is, in RF terms, usually a "class C" one-transistor stage where the base is driven hard by a uC pin. The signal will be reduced in amplitude if the LC is out of tune. So it can make sense to also peak this LC circuit to get the most onto the line but it won't change the frequency.
But a lamp module is only a receiver.
Regards, Joerg