Allegedly, on or about 12 December 2017, Robert Nichols sent:
You can do that with cryptsetup-reencrypt, but it needs to be able to make space for the ~2MB LUKS header ahead of the filesystem in the partition. That's a fairly risky operation -- shrinking the filesystem slightly and shifting it over. An alternative is LUKS with a detached header, but maintaining that relationship is an administrative headache with a severe penalty for error.
If they had the spare drive space, I'd suggest shrink the existing partition in half. Make a new encrypted one in that new space. Copy the files over. Erase the previous partition, and either keep it for the next lot of jiggery-pokery, or expand your new one into the space.