I too have Liftmaster 8500 jackshaft garage door openers, each included a two-bulb wireless remote controlled luminaire.
I guess some people don't read the directions, where it specifically-states: "Do not use LED bulbs!" This is for the 380LM twin-bulb light, which may be different from yours.
Full disclosure: I read it, and tried it anyways, and no, it gave me problems too. I did place a flourescent bulb in the fixture, which lit and programmed perfectly. However the LED bulb would not function reliably, so I proved to myself, "the factory is right!"
I have 4000K flourescent bulbs in two 380LM remote-controlled lights, they programmed easily, and they work as-designed. I even played-around with the lighting interval before shut-off to see it work. They are a source of interest for our 5 y.o. grandson, getting them to turn-on by proximity, and the timeframe to extinguish. Great fun for him, and another way to get him interested in 'shop things.'
I have the Costco 4 ft LED shop lamps, the 'two-bulb' integrated design, in close-proximity to one of the 380LM lights, and apparently it doesn't seem to affect the Liftmaster light remote-control in the least. The closest point of the Costco LED twin bulbs is probably less-than two feet from the Liftmaster luminaire. The only time I had a signal-issue and interfering with programming of the Liftmaster luminaire was when the LED light was screwed-into the Liftmaster luminaire.
I ran-across a Liftmaster 380LM fixture at Habitat for Humanity, and I was racking my brains for something cool to be controlled by the remote actuation circuit, maybe a recording of "Hail to the Chief" or a soundtrack of Formula 1 cars running through the tunnel at Monaco, I dunno. They wanted $19 for it.