We've had a lockable stainless steel mirror-fronted medicine cabinet in the bathroom for around 10 years (grandchildren...).Today I couldn't turn the key to unlock it; a squirt of WD40 was unsuccessful in freeing the lock.
I could just get a gap of 4 - 5 mm between the door and the cabinet body. It was enough to see the lock arm fixed behind the edge of the cabinet, but also a partially-obscured nut of 20 - 25 mm AF which held the lock to the cabinet door (through the mirror and SS). None of the spanners I had would fit through the gap, but I found a thin spanner (something for a self-assembly job, perhaps) which would go through the gap. Unfortunately it was only about 17 mm across the flats, so I spent
20 minutes with a Dremel and grinding disc to open it up enough to fit over the nut.
It was a bit awkward accessing the nut to turn it, but I got it unscrewed as far as possible until it hit the lock arm. Although it was then possible to pull the lock body away from the door a few mm, it would still not turn as it was held by two flat areas which extended to the lock arm. A bit puzzled what to try next, I got a hacksaw blade and put it in a "sliding" handle and tried cutting through the lock arm on pull strokes. After a dozen strokes the arm suddenly came loose in the lock. Perhaps it was the vibration caused by the sawing. I was able to open the door and get the lock out completely to examine it. The lock arm was held onto the lock body by a screw, which is why it hadn't come free when the nut reached the end of its travel. I took it all apart and then reassembled it. Of course the key now worked perfectly and there seemed absolutely nothing wrong with the lock!
I think that the lock is one of these: