RORY: She’s letting you go? That’s amazing. What changed her mind?
LANE: I let her watch the Romeo and Juliet movie with Leo and Claire Danes.
Lane is talking about William Shakespeare’s Romeo and Juliet (often shortened to Romeo + Juliet), a 1996 film directed by Baz Luhrman and starring Leonardo DiCaprio and Claire Danes in the title roles. It is a modernised adaptation of Romeo and Juliet, with the Montagues and Capulets two rival (mafia) business empires in the fictional American city of Verona Beach (inspired by Venice Beach in L.A., but filmed in Mexico).
The film was a commercial success and gained mostly positive reviews, as well as winning several awards internationally. At the BAFTA Film Awards, it won Best Direction, Best Adapted Screenplay, Best Film Music, and Best Production Design. It continues to be a popular choice for high school English teachers to show their students as an introduction to the play.
It wasn’t released on DVD until 2002, so I’m not sure how Lane showed her mother the movie. Perhaps it was conveniently on at the local cinema.