In addition to examples given in the previous answer, another similarity between these two characters is the fact that they are both white girls that end up in storylines in which they learn about the complexities of the African American experience, and racism in America.
In To Kill a Mockingbird, Scout witnesses the trial of Tom Robinson, a black man who was falsely accused of raping a white woman named Mayella Ewell. Over the course of the trial and its aftermath, Scout learns about segregation and the toxic and often violent nature of racism.
In The Secret Life of Bees, Lily also sees the violent nature of racism, as she witnesses firsthand the beating and arrest of her African American caretaker, Rosaleen, when she tries to register to vote. As the story moves on, over time Lily forms meaningful relationships with the Boatwright sisters and learns a lot about their life experiences and about prejudice in her relationship with June. Additionally, Lily and Zach get close to having a romantic relationship, but decide to hold off because of the possible repercussions of being an interracial couple.
There's also the fact that both girls live in the Southern US— Scout in 1930s Alabama, and Lily in 1960s South Carolina. Both of these settings make a lot of sense for plot lines with that focus on racial tension.