Between takes on the set of “Billions,” Damian Lewis is standing amid a sea of Bloomberg computer terminals singing Hall & Oates to no one in particular. “Because your kiss, your kiss, is on my list,” croons the actor, clad in jeans, Pumas and a gray buttondown.

But don’t let the breezy vibe fool you: In the drama, Lewis plays a cutthroat hedge fund manager and self-made billionaire named Bobby “Axe” Axelrod whose extraordinary track record arouses the suspicions of a combative U.S. attorney, Chuck Rhoades, played by Paul Giamatti. Rhoades’ righteous zeal is tempered somewhat by a giant conflict of interest at home: His wife, Wendy (Maggie Siff), just so happens to be the in-house shrink and performance coach at Axelrod’s firm, Axe Capital.

The series, premiering Jan. 17 on Showtime and co-created by New York Times financial columnist Andrew Ross Sorkin, arrives more than seven years after…