what does may do after she acknowledes that she knew lilys mother

Do you mean what Lily does after this? Lily asks May if she remembers a Deborah Fontanel, and May says yes, Deborah stayed out in the honey house for a while. Lily feels light-headed and goes out to the honey house. Lily becomes obsessed with the idea that her mother walked in the very same room in which she stood. Lily eventually falls asleep.