She appeared as Little Red Riding Hood in Disney's film adaptation Into the Woods. She learned she had landed the big role of Little Red Riding Hood while filming the independent movie Little Miss Perfect.

Before appearing on the big screen, Lilla made her Broadway debut starring as Debbie in the Tony Award-winning musical Billy Elliot, directed by Stephen Daldry. Then, in 2012, she was cast from a nationwide search of over 5,000 young performers in the title role of the 35th Anniversary Broadway revival of Annie, directed by James Lapine. She garnered award nominations from the Drama League, the Outer Critics Circle, and Broadway.com's Choice Awards for her portrayal of the famous red-headed orphan.  

Lille has performed in numerous readings and benefit concerts, including The New York Philharmonic's One Singular Sensation: Celebrating Marvin Hamlisch; the musical Home, directed by Stafford Arima, written by Scott Alan, and co-starring Dianne Ladd; and Ragtime at Avery Fisher Hall co-starring Broadway stars Tyne Daly, Norm Lewis, Lea Salonga, and Patina Miller.