Can a set of show tunes and Great American Songbook standards, rendered with a healthy measure of respect and virtuosity, also be a punk-rock show? Or at least something that kinda/ sorta feels like one?

That basic question arose over the course of seeing Lady Gaga’s secret post-midnight performance at downtown L.A.’s movie-palace-turned-music-club, the Belasco. There are surely a few performers out there who have a feel for both the classics of the Broadway/movie-musical era and raw-power rock ‘n’ roll. They just don’t exist at anywhere near the superstar level, and even in a more niche world, they probably know better than to try to combine these extremely different ethos. Lady Gaga, thankfully, does not know any better. After catching Monday night’s show, I’m happy to report that she is the woman who can marry the controlled genius of Tin Pan Alley and...