Update: We updated our Lumerical installation and the issue is still persisting (previously we were using v2020 R2.4, I believe).
Now, instead of getting stuck indefinitely, it is giving us an error (still at the same point in the code though):
lumapi.LumApiError: 'appOpen error: \n Failed to start messaging, check licenses...'
As far as I am aware, there have been no changes to our license. When we check the Ansys license manager log, we don't see any errors.