Sullivan grew up in Queensland and attended John Paul College in early years then went to Calvary Christian College in year 2 in Logan, graduating in 2011. Her father is an importer of medical equipment, and her mother is a visual artist. She has one older brother, Edward. She has family overseas, particularly in Britain, from where Sullivan’s parents emigrated. 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.

In 2018, she reached further prominence in the lead role of Miranda in Picnic At Hanging Rock. Later that year, she became the face of Australian pearl company Paspaley, starring in a 60 second advertising video shot on the Kimberley Coast.