When we had a replacement garage door installed last year the installation firm (who were great.....if you are in the Toronto area they are mentioned in a couple of garage weather stripping articles we wrote on our blog in early May and I highly recommend them) simply used an extended pair of frames for the garage door.
Our garage ceiling is also around 11 feet high.
So, the garage door rolls up out of the way for the lift and for us who use the stairs coming off the lift platform.
Here's a posting from our blog showing the before and after the installation of the lift and the new garage door.