We got a few recommendations for epoxy for our lock and J-B Weld topped everyone's list.
We took pictures of the inside of the lock before Rob took it apart. The first attempt at gluing failed because there was nothing holding the two pieces together besides the epoxy. Rob set an x-acto knife blade inside the lock and glued the two pieces to that. Big improvement, but still not super secure.
After scavenging around in the basement he found another thin piece of metal that he wrapped around the outside of the mortise and cold welded in place.