The director was very excited to speak to the actress when he stopped off at her table during the 98th Annual White House Correspondents' Association dinner in Washington D.C.
After being introduced to the 'Mean Girls' actress, he said: "I feel like a kid, because I'm so excited to meet you."
Lindsay enjoyed chatting to Diane Keaton at the dinner - which was also attended by Kim Kardashian and her mother Kris Jenner, Elle MacPherson, Josh Hutcherson, Mary J. Blige, Goldie Hawn and Eva Longoria - and George Clooney also said hi to the blonde star.
The 25-year-old beauty - who is infamous for her legal and drug problems - attended the event with Fox News anchor Greta Van Susteren, who revealed Lindsay is "passionate" about her acting career.
She told the New York Post newspaper: "Lindsay is passionate about movies and her work. You mention the art of moviemaking, and she really digs into the topic. We had a long talk about movies in the car as we were stuck in traffic.
"Many people only get to see Lindsay through the eyes of the media, but it was a totally different experience to sit down and have a conversation with her."
During a visit to the ladies' room at the dinner, Lindsay gave an elderly Hispanic cleaner called Bianca $100 and told her, "you're too old to be doing this".
The attendant initially refused the kind gesture, but Lindsay insisted she accept her gift and pushed the cash into her hand while saying, "Please, you're too old to be doing this kind of work."