Patricia Clarkson is an actor who always hits the true note, but it’s been quite a while since she nabbed a movie role as full-scale and invigorating as the one she has in “Lilly.” The movie, which opened yesterday, is a whistleblower drama, based on the life of Lilly Ledbetter, who was the image of a homespun citizen — an Alabama wife and mother working as a supervisor at the local Goodyear Tire & Rubber Company plant — when she became an activist almost in spite of herself.

At Goodyear, Ledbetter started out in 1979 slinging tires on the factory floor. She then climbed the managerial ladder, only to keep getting knocked back down. Her work record was top drawer, but she was the only supervisor at the plant who was a woman, and that made a lot of people around her nervous. Near the end of her 20 years there, she learned she...