It depends on if the bottom of the door (when up) is the issue or the opening is the issue. My door hangs down a little below the opening and inch or two. Not a problem as I don't have a lift. But, the door height can be adjusted by adjusting the springs - if you have the type of door with the springs across the top of the header. Caution - you have to be very careful when playing with the springs - get some winding bars and learn how to adjust - there are several youtube videos on this.
If that won't give enough clearance, then you could raise the header like one member did a few years back. It's a lot of work though!