Rapp grew up in Santa Rosa, California and attended the American Academy of Dramatic Arts on San Francisco in 1994, where she studied theater. At the advice of one of her instructors, she began taking classes in voice acting, landing parts as children and toys.
Her first paid job as a voice actor was in 1999, and in 2003 she was cast to provide voices for children for The Sims franchise. Rapp was cast as Lili in the 2005 game Psychonauts.
She was cast to provide the voice of Morgan LeFlay in the 2009 title Tales of Monkey Island, developed by Telltale Games. Telltale Games cast Rapp in a second game, Sam & Max: The Devil's Playhouse, where she provided the voices of Sammun-Mak and Sam Jr., a cockroach. Rapp also provided the voice for Lilly in the 2012 game The Walking Dead, her third casting by Telltale Games.
- The Walking Dead - as Lilly Caul
- Tales of Monkey Island
- The Sims
- The Wolf Among Us
- She seems to have a knack for dubbing characters with the name Lilly or so, as she provide the voice for a character named Lili, Lilly and Lily in Psychonauts, Telltale's TWD and Firewatch, respectivly.