How does the quote at the beginning of chapter 12 relate to Lily's anguish?
This is an important question. It is a good idea to pay attention to the quotes at the beginning of each chapter.
Now, you will notice that the queen bee is characterized as the "mother" of the hive, is described as "spending her days in darkness" (232), and does not appear to have any "maternal instincts or ability to care for her young (232).
It becomes clear that Lily's mother, Deborah, while she loved Lily deeply, was very much like the queen bee. As Lily learns the truth about her mother, she is anguished about how the past led her to her present state, a feeling of great loss and confusion, and the pain of not having a mother.
What are the similarities between Deborah and the queen bee? The world of darkness in which the queen bee exists is much like the world of darkness in which Deborah existed. We can see that Deborah suffered from clinical depression, which is characterized by many who suffer from it as a kind of terrible darkness. Also, because of the differences between Deborah and T. Ray, her marriage was a world of darkness, as was her existence on a remote rural farm. Now, a person who is living in such a dark world is not necessarily someone who is prepared to be a good parent. Deborah appears to have been very young when she had Lily, and might not have had the wherewithal to be a good mother and fight the darkness within her and around her. New mothers also need support, and it is unlikely that she had much support from T.Ray or her community. So in this way she was like the queen bee, who is a mother without the instincts or skills necessary to be a mother.
It was these aspects of Deborah that led to her running away from her situation, toward someone who had been able to mother her in the past, August. Of course, her return to the household resulted in her death, which was really no one's fault, but which did lead to Lily's painful years of growing up. For Lily to learn that her mother was willing to leave her is even more painful.