Willowood / by Cecilia Galante.

Enhanced descriptions from Syndetics:

There's nothing ten-year-old Lily Sinclair likes about her new life in the city with her single mom. She misses her best friend, who seems to have forgotten her and their secret place, Willowood. She never sees her mom, who's working long hours at her new job. She's managed to make an enemy of the class bully. Mrs. Hiller from across the hall, who takes care of Lily after school, keeps preparing yucky healthy snacks for her. And she can't get her mother to tell her anything about her absent father. Her only source of comfort is her beloved pet gecko, Weemis. Everything changes when Mrs. Hiller introduces Lily to the owner of the Pet Palace, a nearby pet store, and his adult Down's syndrome son, Nate Lily finds herself with an unofficial after school job--and forges a tentative friendship with Nate that's threatened by a dark secret about Nate Lily knows nothing about.