There's an odd thing about operatic titles. The ENO would always say The Marriage of Figaro,
...or, in the case of the production-before-the-production-before-last, "Figaro's Wedding" - which is semantically more accurate but which I found affected and pretentious.
But there are some which are never translated, as untranslatable, Traviata, Trovatore, Cosi fan tutte, Freischutz, Boheme.
Of that list I'd say Trovatore is an odd one out, as it
is straightforwardly translatable. But nobody ever does.
I get the impression that if there was not a standard English translation of the title in the past, then the original is used. Lucy of Lammermoor is the unambiguous and accurate translation of the work the ENO is calling Lucia di Lammermoor.
I certainly wouldn't want the title to be given as "Lucy of Lammermoor" unless the sung translation were also to refer to Lucy, Henry, Edgar, Arthur and so forth. Which would make it even much more difficult for the translator to find English phrases which complement the musical line.
As to the original question - Madam or Madama or Madame Butterfly - I would expect that a listing in England for an Italian-language performance would be given as Madama, but that an English-language performance would be given as Madam (not Madame, despite the fact that the source text was so called). Of course this probably doesn't help if the listing is for an excerpts concert, given that perhaps the most popular excerpt has neither Italian nor English words...
