You might find it useful to re-read Chapter Seven, which is the first time when Zach and Lily actually meet and get to know each other. What is interesting is the immediate way in which Lily feels drawn to Zach and how handsome she finds him. Lily recalls the way that she used to laugh at jokes her white friends used to make about black people and their appearance, but note how seeing Zach challenges her former ideas about black people and beauty:
At my school they made fun of coloured people's lips and noses. I myself had laughed at these jokes, hoping to fit in. Now I wished I could pen a letter to my school to be read at opening assembly that would tell them how wrong we'd all been. You should see Zachary Taylor, I'd say.
So, not only is Lily struck by how handsome Zach is, at the same time let us remember that Zach is the only person who is a similar age to Lily, and therefore it seems clear that they would spend lots of time together and be able to interact in a way that Lily is unable to with others. I think it is important as well that Zach, like Lily, is shown to be an outcast of white society in the way that he is arrested for being black. Lily feels a certain amount of sympathy with him in this respect, as she feels that she is an outcast from white society too in the way that she has run away and also through the memories she has of her mother. These reasons all serve to bring them together and create lots of mutual sympathy between them.