What fact from the past brings August and Lily so lovingly together in The Secret Life of Bees?
I assume you are refering to the revelation of Chapter Twelve, which is when Lily and August finally have a long-anticipated discussion about Lily's past and in particular her relationship with her mother. It is in this chapter that Lily discovers that August had known all along that she was Deborah's daughter, and in fact that she had worked as the housekeeper for Deborah's family and had therefore developed a very close friendship with Deborah. August tells Lily that she knew Lily's mother incredibly well:
"I used to take care of her," August said. "I ironed her dresses and packed her school lunch in a paper bag. She loved peanut butter. That's all she wanted. Peanut butter Monday through Friday."
This shared relationship with Deborah, Lily's mother, is the fact that unites August and Lily together and helps Lily to begin to process the whole gamut of feelings and emotions she has about her mother. It is what August tells her about Deborah and the objects that belonged to Deborah that she gives to Lily that help start this process.