why does lily think August told her the story of Beatrix the nun?

The story of Beatrix in meant to teach Lily a lesson. August wants her to understand, that no matter what happens in this life faith will bring her through. Beatrix was a runaway nun, but her faith in Mary (along with Mary's help) and the fact that she finally asked for helped, allowed her to know she wasn't alone. Through this story and their talk, August assures Lily that if she asks for Mary’s help, Mary will provide what she needs. Lily asks Mary for assurance that she will never have to return home and that the police will not apprehend her and Rosaleen.

The story of Beatrix in meant to teach Lily a lesson. August wants her to understand, that no matter what happens in this life faith will bring her through. Beatrix was a runaway nun, but her faith in Mary (along with Mary's help) and the fact that she finally asked for helped, allowed her to know she wasn't alone. Through this story and their talk, August assures Lily that if she asks for Mary’s help, Mary will provide what she needs. Lily asks Mary for assurance that she will never have to return home and that the police will not apprehend her and Rosaleen.

And this sums it up!