I have been wodnering this too. One of the first threads I started was about how Lips could play the trumpet.
Whenever he plays, his fingers move. I always thought that his arms were controlled by wires, but I never see any arm wires on him. I have noticed that he has big sleeves, which could possibly hide the arms of a puppeteer (similar to how the thing hanging from Dr. teeth's wrists hide his performers arms). Also, when his sleeves are more skin-tight, like when he wears a tuxedo, his elbows still normally touch the bottom of the screen. But I have also seen a photo of Steve Whitmire performing Lips, and in that photo0, it looked like he had arm wires (it sort of looked like they are connected to the elbows, which would be a weird way to connect them).