Mine will stick in the down position only, whenever it wants to. I have to pop out the switch panel and tap on the motor just a little and up it comes. Only sticks when I take it all the way down. Might be weeks before it sticks again , but always with the same results. I'm baffeled.
If you take the side of the door skin inside the door, it is the mechanism that raises one of the lower window, run window up and down, you'll see what I mean. Keep hands out of the door when you run it as you may be less of a finger or two! Regarding lubricant I think the white lithium grease would do.