He was reportedly named after Levon Helm from the rock group The Band, a musical hero of his father.
[10] On his mother's side, he is a grandson of Buddhist scholar Robert Thurman and model Nena von Schlebrügge.
[11][12] Schlebrügge's mother, Birgit Holmquist, was also a model, having posed for Axel Ebbe's statue Famntaget, installed in the harbour of Smygehuk in Sweden, in 1930.
[16] Hawke has a role in the ensemble cast of Apple TV+ anthology series The Crowded Room alongside Tom Holland.
[20] In September 2024 Levon made his directorial debut with Picture Day a play written by him and performed at Coffey Street Studios.