Try all your keys you already have and use wd40.

1) check the back of the coin door. Is it hanging on a hook?
2) check inside the cabinet. Is it hanging on a hook?
3) Inspect the cabinet as much as possible--maybe the key fell inside somewhere?
4) Is there a 3 or 4-digit number visible on the lock? That's the key you have to find.
5) Try any double-bitted keys that you might have.
6) You can try to pick it. Note--I can pick single-bitted locks without too much difficulty, but I find double-bitted locks fairly challenging. The lock's age and stiffness makes it even more difficult.
7) drill the lock, but not all the way through to the retaining screw. Just try to get all the lock bits, jam a large flat head screwdriver in the hole, and turn.
8) If you drill all the way through and the screw pops out, use either a matching square screw bit or a large flat head screwdriver and try to jam it in the square hole of the bracket, then try to turn it.

Drill the lock tumblers. Use a bit about the same size as the slot. Will be a double bitted lock, so you'll have to drill tumblers at the top and bottom of the slot. You'll feel them give way as you drill through them. Drill on top and bottom, blow out shavings, try to turn with a big standard screwdriver. If you can't turn by hand, drill tumblers more. Messy and tedious, might take a few tries, but eventually you should be able to turn the lock and mechanism.

Don't do this. Take your time and drill the tumblers. Doesn't take long with a sharp bit.

This times 1000. I always see people thinking they need to drill out the entire cylinder and punch out the screw/lock arm on the back, but you only need to very carefully drill the sheer lines. Much easier and less messy.

You can also learn lock picking which is scarily easy.

I'm good with picking locks and even have a pro set of tools from a locksmith buddy, the double-bitted ones are a bear. I dont even waste my time anymore past 2 minutes. Either it picks right away or I get the cordless drill out.

Single bit? 30 seconds flat I can pick.

Drill baby drill!

It depends. On the front door locks, you only need a drill bit just large enough to drill through the lock and take out the lock arm screw. Removing tumblers takes much larger drill, and there might be problems due to debris left in lock mechanism.

On the backbox locks however, it might be better to try getting rid of the tumblers and leave lock arm intact. Drilling through the lock arm screw can make it very difficult to turn the backbox hinge/glass holding lever.

I dunno, I use much smaller bits for sheer line drilling than the screw in the back.

The lock in the picture doesn't appear to be double bitted though, it looks to be single bitted.

That is indeed true, if you can drill carefully both sides one at a time. I was thinking of a single drill straight through the centre.

Having an ample collection of "Fort Lock" keys is also a great help. Very often a random old key opens the lock with a little persuasion.

Check the cabinet very carefully, it’s probably screwed inside the cabinet somewhere. My Caveman has one screwed right in and the number was actually written on the side as well.
Drilling those can be a total pain. You can usually get away with a bump-key method, putting slight tension and wiggling a key or a pick and getting them open, I just did it yesterday with a double-bitted lock. Maybe 4 minutes effort? And then it’s nice because I can just compare the pins to the keys I have, many times they’re just stuck and I don’t have to waste a lock (I’m cheap)