At this point, it's probably more surprising that Lady Gaga hasn't recorded a full Christmas album yet, multiple years and lots of inescapability into her career. But she's said that's changing. Just in time for June!
Gaga told Stephen Fry (there's a pairing you didn't expect) in the Financial Times that she wanted to do an album of "GaGa and the jazz standards." We're not sure what that first part means, unless she plans on adding Gregorian-chant "Gaga"s like "Bloody Mary".
It also isn't clear whether these are Christmas standards or just jazz standards that happen to be coming out on Christmas to snatch up the No. 1 spot that day. If it's the former, though, give it a few years and it'll be grudgingly accepted into the Christmas canon, the same way Britney Spears' "My Only Wish" was and the way Mariah Carey's "All I Want For Christmas Is You" unquestionably has been.
Or, put more precisely, the same way Gaga's already-extant "Christmas Tree" didn't. It only came out a few years ago, but still: a The Fame-y number that could hardly be called a "jazz standard," unless maybe you meant the original meaning of the word "jazz." Relive it below, and see what coal you might not get this year: