Gavin O'Connor will direct the film, which has a script by Bill Dubuque, about a government accountant who doubles as an assassin.
Lithgow will play Lamar Black, a tech magnate who hires Affleck's character to look into his company's finances.
Lithgow is a two-time Academy Award nominee for "The World According to Garp" and "Terms of Endearment." He won Tony Awards for The Changing Room and Sweet Smell of Success and was Tony-nominated for Requiem for a Heavyweight, M. Butterfly, Dirty Rotten Scoundrels and The Columnist.
Lynette Howell and Mark Williams are producing, and Jamie Patricof and O'Connor are executive producing the film.