1) I'd check that the bulbs are good. Put the bulbs into a lamp that you know is working. Try the old ones first, if they do not work, test the new ones. It's a stupid check but it is quick, easy and can save alot of trouble shooting time if it is the problem.

2) Check that the bulb sockets and contact points are clean on the opener. Also check that the bottom connector is not broken and sits up enough that it would touch the bottom of your bulbs. If dirty looking, clean them. If contacts are laying too flat, gently bend them slight upwards. Retest with a known working bulb. If it fails, to check your sanity, recheck that the bulb is still working in a known working lamp.

If the above two checks don't fix it you have some type of circuit problem in the unit. It is getting power as shown by the door working, but the lights are not getting power.

One remote possibility is that maybe the lights are wired in series, where all bulbs would have to work for the circuit to work. However, I highly doubt they would design the unit this way. I hope it is just a bulb or contact problem for your sake. These things sound like a pain to troubleshoot.