Cobb had studied at New York University when he joined the left wing Group Theatre in 1935 and appeared in its production of Clifford Odets' play Waiting for Lefty. In 1937 he made his movie debut in Ali Baba Goes to Town. He is probably best known for creating the role of Willy Loman in Arthur Miller's stage play Death of a Salesman directed by Elia Kazan.

He also played James Coburn's supervisor in the psychedelic flicks, In Like Flint and Our Man Flint. He was in the original live TV movie, "Death of a Salesman" which included then unknown actors like Gene Wilder, Bernie Kopell, and George Segal. Cobb was nominated for an Emmy Award for the performance.

Cobb was named as a possible Communist in testimony before the House Un-American Activities Committee because of his involvement in the Group Theatre. He was called to testify before HUAC but refused to do so for two years until, with his career threatened by the blacklist, he relented in 1953 and gave testimony in which he named twenty people as former members of the Communist Party USA.

Later, Cobb explained why he "named names" saying:

"When the facilities of the government of the United States are drawn on an individual it can be terrifying. The blacklist is just the opening gambit - being deprived of work. Your passport is confiscated. That's minor. But not being able to move without being tailed is something else. After a certain point it grows to implied as well as articulated threats, and people succumb. My wife did, and she was institutionalized. The HUAC did a deal with me. I was pretty much worn down. I had no money. I couldn't borrow. I had the expenses of taking care of the children. Why am I subjecting my loved ones to this? If it's worth dying for, and I am just as idealistic as the next fellow. But I decided it wasn't worth dying for, and if this gesture was the way of getting out of the penitentiary I'd do it. I had to be employable again." (Inteview with Victor Navasky for the 1982 book Naming Names.) Following the hearing he resumed his career and worked with Kazan and Budd Schulberg, two other HUAC "friendly witnesses" on the 1954 film On the Waterfront which is widely seen as an allegory and apologia for testifying. Other notable films he's appeared in include The Left Hand of God (1955), Twelve Angry Men (1957), Man of the West (1958), The Brothers Karamazov (1958), Exodus (1960), How the West Was Won (1962), Coogan's Bluff (1968) and The Exorcist (1973), his last movie.

Cobb also appeared as ranch owner Judge Garth in the television series The Virginian.

Lee J. Cobb died of a heart attack in 1976 in Woodland Hills, California and was buried in Mount Sinai Memorial Park Cemetery in Los Angeles.