Here's how Lily gets to Tiburon:
1. Escape from home: Lily runs away from her abusive father, T-Ray, after he assaults her mother.
2. Rosaleen's arrest: Rosaleen, the black woman who works for Lily's family, gets arrested for defending Lily from a racist attack.
3. Leaving for Tiburon: Lily, feeling responsible for Rosaleen's arrest, decides to go to Tiburon to find the "Black Madonna" mentioned in a letter from her mother.
4. Meeting the Boatwright sisters: Lily and Rosaleen, hitchhiking, are picked up by Zach, who takes them to the Boatwright sisters' house, where they are welcomed in.
T-Ray never comes to Tiburon searching for Lily. He is unaware of her whereabouts and remains in their home in Sylvan, South Carolina. The film and book focus on Lily's journey towards healing and self-discovery, not on any pursuit by her abusive father.