So far as I know, the lift simply runs at intervals, no switch. Or if there is one, I want to know too!
I'd just ignore him, or else start trying to gauge some combo ASDM shots to his altitude. Might take a while to get the right distance. Or you could get the minigun, and wait for him to fire a redeemer at you, then fire back with the minigun and explode his Redeemer in his own face.