Sullivan grew up in Queensland and attended Calvary Christian College in Logan, (near Brisbane, graduating in 2011. Her father is an importer of medical equipment, and her mother is a visual Artist. She has family overseas, particularly in Britain, where Sullivan's parents emigrated from. She was a runner-up in the 2015 Heath Ledger Scholarship to attend Screenwise Film and Television School.

In 2014, she appeared in the feature film Galore, which premiered at the Melbourne International Film Festival and screened at the Berlin International Film Festival. She earned a Best Supporting Actress award at Cinema des Antipodes Saint-Tropez.

Lily has also appeared in the second season of the television series Rake and in the NBC series Camp. She has a role in Sucker, which was released in late 2015.

Sullivan made her feature film debut in P. J. Hogan’s 2012 feature Mental, earning an AACTA Award nomination for Best Young Actor and a Film Critics Circle of Australia Award nomination for Best Performance by a Young Actor.