I have a 2-car garage, using a single overhead door with opener. The ceiling is about 11.75 ft. I would like to put a residential car lift in one bay. What would it take to raise the overhead door track, so it will provide door clearance over the lifted car?

You would need a hi-lift track system to get the door up to the ceiling, any garage door installer should be able to help you out with it.

Your welcome, let me know if you have any problems, I might be able to help more. I put this in a house for a client for the same purpose as you, only he had a 16 foot ceiling.