This is a rim lock on a swinging "carriage style" garage door from 1925. The lock is terrible, very hard to adjust, and to keep adjusted as seasonal variations occur the spacing. The lock is keyed on the outside.
What type of lock would be better?
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.
Here is a set of doors on a house I am working on they are probably 15-20 years old, been repaired one time. The hardware is very simple, a regular deadbolt, a foot bolt and spring loaded top bolt. After I threw the deadbolt, which locked very easy, I pushed and pulled on the doors, they are very stable for doors that are nearly 8 ft. tall. The active side has a door closer. It is important that the doors at their minimum, no locks, latches. Nothing but the hinges, get that right, make it stable, then add the lock.
I think the diagonal cable is added to torque the door into a different plane so it matches the other door where it meets. Other wise it is on upside down. You may need to add one, or something that does the same thing that will lift the dragging edge that makes the door stick.
Just tossing stuff out there...