Jon, I don't think you can say the winder is broken, it may be. On an LX with sticky mirror, the winder motor will move and push the shutter release (making noise). It will then hang up, waiting for the sticky mirror to release so it can wind the film.
If you want to know for sure, take your LX into the shop. Most sticky mirrors clear up after 2 or three shots and move swiftly. So the LX winder should work OK with a sticky mirror LX after the first 2 or three shaps. Regards, Bob S. Jon asks: >>I happened across a Winder LX on a camera shops website a while back at a seemingly very fair $129 in very nice condition. I was in the vicinity of that shop today and decided to drop in and have a look. I asked for a demonstration of it (I didn't have my camera with me, so the salesman used an LX from the store) which gave puzzling results... It will act like it's at the end of the roll after firing the first shot. The catch here is the camera body they had seemed to have sticky mirror syndrome rather badly. Would a sticky mirror cause a malfunction of the winder? If so, I'm tempted to go ahead and call the shop and have them ship the winder to me. It looked as new, and the price seems right to me.