Is the last key gone forever?

So I finished the game (more or less) by completing the (frankly mind bending) >!Atelier!< puzzle.

Thing is, I never got the last >!Sanctum!< key. You don’t really need all of them, even with one missing and its related content, the associated puzzle is easy to complete.

So I looked it up and now know that it’s the >!vault 370!< key. Amusingly, I had opened every other compartment, including the mismatched number one, but not this one. And for the last 25 days or so of my run since I finished the >!room 46 safe puzzle that needs the Sanctum keys!< I have not seen the vault 370 key pop up anywhere. I guess I just got unlucky to never get that one open on any given day.

Does the fact that I solved that puzzle mean that I can never again find this key, and therefore am locked out of what seems to be a related trophy?