Without Access to the Garage Interior, How Can I Replace the Handle/Lock?
If the lock is separate from the handle and turns freely, my guess is the handle is the issue, not the lock.  Overhead garage doors almost always latch by extending pins through the tracks on either side of the door. It is likely that one of these just got bound due to expansion, contraction, ice lifting, or whatnot. I'd try a couple things before doing anything with the lock itself. First, grab the handle and alternate between jerking the door up and down while you try to turn it.  If this doesn't work, you may be able to carefully remove the trim on either side of the door.  Usually there will be enough of a gap to slide in a flatbar or something similar to tap on the latching pins. If they're stuck, knocking them up and down a couple times will usually free them.