Several of the guys I worked with had 2x2 or bigger angle iron that folded in on the sides, locking all drawers. These were on boxes with full angle frames for regular loading and unloading, so welding some hinges on was no problem. Other choice was a bar that slid down along the front and the lock was either through the bar and the fixed part, or the bar would be captured by a bottom socket and the lock.
Both of those are fine for keeping the casual tool borrower out, but if you're leaving the box unattended in a shop full of other tools, and especially if you've added lifting lugs and the crane is parked a few feet away, the whole thing goes in the back of a truck in about 2 minutes. We had one guy who was going away for a few years, and he welded his box to one of the warehouse I beams. Of course, since it wasn't his shop, my second job (after sweeping the floor) was to cut that box loose so we could use the space, and put it in the back where no one would see it again. The guy died 8 years ago, and last time I stopped by for a visit, the box was still there. I should make an offer...