Lambert started his career playing supporting parts in several French films. He came to international attention, when he took on the title role in Hugh Hudson’s Greystoke: The Legend of Tarzan (1984), which was nominated for three Academy Awards and won a BAFTA Award, as well as a César Award amongst other nominations. In 1985, Lambert played the lead in Luc Besson's stylistic film Subway, alongside Isabelle Adjani, Jean Reno and Jean-Hugues Anglade and for which he won a César Award for best Actor.
Following these successes, he appeared in a variety of films, including Michael Cimino’s The Sicilian (1987) as Salvatore Giuliano, the thriller Knight Moves (1992), Stuart Gordon’s Fortress (1992), the post-apocalyptic action film Beowulf (1999), Richard Kelly’s Southland Tales (2006), and Ghost Rider: Spirit of Vengeance (2011), among many others.
Some of his most recent work includes 10 Days in a Madhouse (2015), the French romantic comedy Un plus une (2015), starring alongside Elsa Zylberstein and Jean Dujardin, Joel and Ethan Cohen’s ensemble comedy, Hail, Caesar!, the martial arts film Kickboxer: Retaliation (2016), featuring Jean-Claude Van Damme, Alain Moussi, Ronaldhino, and Mike Tyson, Konstantin Khabensky’s Russian war drama film, Sobibor (2018), and the hostage drama Bel Canto (2018) with Julianne Moore and Ken Watanabe.
Most recently, he played Bastien Moreau in the sixth season of highly successful crime thriller series, The Blacklist.