Interesting this as double or triple throw makes sense on doors or heavy chests to get more travel or extra engagement of the locking bolts, but makes little sense on a Voyage de Necessaire with a single key as Daniel is asking, as they are generally box-type locks with a link plate and studs on the hinged lid?
They typically need a small amount of travel to engage securely, so double or triple action seems pretty pointless with a lock operated by a single key unless it is actually doing something additional or trick inside.
Doug you made good points on the heavy versions of these locks a while back in another thread, where you said about the matching pierced barrel the key fits being called the ‘canon’, which I wasn’t aware of before.