What style of lock for swinging garage doors that shift with the weather?
The lock is a standard household door lock, not really designed for doors that slop around as much as garage or barn doors do. You'd have to do a bit of jury-rigging, since they are virtually all designed for modern-style roll-up garage doors, but a garage door style lock will have considerably more slop and adjustability. You'd probably have to mount either an actual section of garage-door track, or simply something else with a slot to accept the tongue/bolt to use most "garage-door" hardware.

Here is one I found looking for "gate" locks, described as a "long throw rimlock" (key cylinder on the other side, this is the inside view) that would not appear to require jury-rigging. Note that there is considerable room for the parts to move up and down or side to side while still locking.