Symptom: After the garage door closes the lights will not go out. Pressing the wall switch will not turn them off either.

Most likely solution: the relay controlling the lights is stuck in the closed position.

Here is the garage door opener, its internal parts exposed:

There is a board for the I/O, remote (the one parallel to the ceiling) and one to control the motor and lights (perpendicular to the ceiling).

Note where the blue and white wires connect on the board (those wires go to the lights).
You can the follow the traces on the circuit board to see which relay they go to.
The relay is a Song Chuan 801H-1A-C.

I bought mine at mouser.com and here is a link to the specification sheet (PDF).

Remove the board:

remove the relay:

and put the new one in.

  

Put the board back in the garage door opener.