Their first musical partnership was a sassy take on “The Lady Is a Tramp” in 2011. Now Tony and Lady (as they call each other) have recorded an album, Cheek to Cheek, due Sept. 23; highlights include buoyant duets on “Anything Goes” and the title track, as well as powerful solo renditions of “Sophisticated Lady” (his) and “Lush Life” (hers). “These songs never go out of style,” Bennett says. “Like a good black dress!” adds Lady Gaga (née Stefani Germanotta). The duo sat down in his art studio (Bennett is an accomplished painter and watercolorist; the home he shares with his wife of seven years, Susan Crow, is nearby) to talk about music and how he helped her through a troubling time when, she says, “I didn’t even want to sing anymore.”