Jennifer Lawrence and David O. Russell make up perhaps one of today’s most famous director-actor duos. But that partnership almost didn’t happen.

Speaking at the Tribeca Film Festival Saturday night for its Directors Series, Russell revealed that Lawrence was the last person cast in both their first movie together, “Silver Linings Playbook,” and their second, “American Hustle.”

For “Silver Linings,” Russell said, “we thought you were too young and there were other actresses in the front of the line who were close to getting the role.” As for “American Hustle,” however, Lawrence was busy with other movies and “technically not available.”

“I called her up on her vacation and I said, ‘I feel like I would be remiss as your friend if I did not give you one last chance to say no to this role,” he recalled. “You said, ‘will I get to have big hair and long nails and be crazy?...