The epigraph at the beginning of chapter 14 simply means that a hive of bees without a queen can become a very sad and mournful place. In a beehive, the queen is the giver of life. Without her, the other bees have nothing to live for. But great change can also occur from the introduction of a new queen into the hive. That's the literal meaning of the epigraph. The metaphorical meaning refers to Deborah's abandonment of Lily. Deborah, the queen bee, as it were, has departed the "hive," leaving Lily feeling sad and mournful. Without the queen bee, or mother, the hive or home just isn't the same.
Nevertheless, August admirably fulfills the role of queen bee herself. She also encourages Lily to cultivate her innate spirituality as a way of making herself feel whole again in the wake of Deborah's departure.