Haydn began her career as a child Actress at the age of seven. She initially appeared in commercials and moved on to television and film roles. From 1979 to 1980, she played Jenny Columbo, daughter of Lt. Columbo and his ex-wife, Kate Columbo/Callahan (Kate Mulgrew) in the Columbo spin-off series Mrs. Columbo. In 1983, she starred as Belinda Capuletti, the smart and sassy daughter of Rodney Dangerfield's character in the comedy film Easy Money. She also appeared in the first Not Quite Human TV movie in 1987, and was a regular cast member on the syndicated sitcom The New Gidget.

Haydn began playing the violin at the age of eight. She played her first professional gig in 1990. In 1992, Haydn graduated from Brown University with a B.A. in political science and began to pursue a career in music. Her debut album, Lili, was released in the fall of 1997 and was followed by Light Blue Sun in 2003 and Place Between Places in 2008, which she promoted with television and radio appearances such as The Tonight Show with Jay Leno, and NPR. NPR described "Place Between Places" as "A mix of neo-psychedelic flower child and rock star virtuoso...Heifetz meet Hendrix." She contributed to the score of the Edward Burns/Jennifer Aniston film She's the One (1996), as well as several films with Hans Zimmer, including Disney's Pirates of the Caribbean: At World's End.

After graduating from Brown University with a B.A. in political science, Haydn started composing original songs and became one of the most requested session violinists around Los Angeles. By the time she signed with Atlantic in 1997, she had embraced a variety of genres, having played with Quwaali musician Nusrat Fateh Ali Khan, Porno for Pyros, Tracy Chapman, The Jayhawks, Brandy, Tony! Toni! Tone!, No Doubt, Tom Petty and more. In addition, she has played with, sung with, and opened for Sting, Josh Groban, Herbie Hancock, Robert Plant & Jimmy Page, Matchbox 20, Seal, and George Clinton, who calls her "the Jimi Hendrix of the violin".

In 2008, Haydn accompanied Roger Waters at the Coachella music festival when they played "The Dark Side of the Moon". Haydn also performed on Cyndi Lauper's True Colors Tour 2008. That same year she appeared on the cable TV series, Californication. In 2009, Haydn sustained neurological damage after being exposed to the pesticide Chlordane. While she was unable to write lyrics, she was still able to compose music. For the five years, she continued working on film scores and composed music for her fourth album, Lililand, released in September 2014.

Haydn won a fellowship to the Sundance Film Institute composing in 2009, and has composed the film scores for three films, Jacklight, The Horse Boy (premiered at Sundance Film Festival and released in 2009 by Zeitgeist Films), and "The Lightmaker".