Graham, an Irish American, was born in Honolulu, Hawaii, the daughter of Donna Grant, a fashion buyer, and Lawrence Graham (Lauren is named after him), a candy industry lobbyist who was the former President for the chocolate and confection industry association. Her parents divorced when she was five, prompting Graham and her father to move to the D.C. area, where he became a congressional staffer. Graham traveled extensively with her father while growing up.

Graham discovered acting while in elementary school and further honed her talent at Langley High School, where she took part in the drill team. Yet she excelled on the stage, and Graham quickly took to acting in community theatre and other small productions. Graham graduated from Barnard College in 1988 with a Bachelor of Arts degree in English. After moving to Texas in 1992, she earned a Master of Fine Arts Degree in Acting Performance from Southern Methodist University.