Are garage door locks that cannot be opened from the outside available

This looks to be like a schlange or kwikset lockset commonly found at Home Depot. You can easily re-cylinder this, but it isn't obvious how to get the lock off.

My solution was as follows:

1. Rotate the lever to the vertical position. There will be two screws hidden under it.
2. Remove them, and separate the lock into two halves.
3. The lock-half has a cover on it. Remove it.
4. There's a screw that holds the cylinder in.

You can also get a lock/lever combination, as well as new doorknobs -- in many cases you can re-use the existing deadbolt and striker latch and just change the visible hardware.

That's a Euro-style lock cylinder. It is normally held in place by a setscrew clamping it into the lock, but you may have to substantially disassemble the lock before you can get to that screw.

If you can't figure out how to remove the cylinder, I'd suggest dismounting the whole lock body from the door and bringing it to a locksmith. That will save you the "on site service" fees.

Rekeying double-sided Euro cylinders is a skill not all locksmiths in the US have. Single-sided, with keyway on one end and thumb turn on the other, are simpler.