Lily, as you note, starts out to find out about her mother, but her journey results in self-knowledge. There are many reasons this happens.
First, Lily's journey ends in a place where her mother has been known and loved, as an adult and also as a child. This gives Lily knowledge about her mother that she would otherwise never have had. Since we are all part of our parents, in a figurative and literal sense, our knowing and understanding of them is an important part of our knowledge and understanding of ourselves. August and her sisters are able to fill in the blanks for Lily, about her mother as a child and what happened to her mother when she left T-Ray. This more complete picture of Deborah helps Lily to see her mother as a human being with her own needs and frailties, which is important because part of growing up is being able to see our parents as individuals, not just as our parents. This also helps Lily to accept what happened to her mother and allows her to gain some acceptance of herself. Now that she understands what led up to the day her mother died, she is able to forgive herself.
Second, Lily's journey exposes her to a different place, different people, different experiences, and different ideas. This allows her to examine her own ideas and feelings with a new perspective. She learns about community, from the Boatwrights, the bees, and the Daughters of Mary. She learns about the grace and beauty of hard work. She learns that people have problems and flaws, but they can manage to love one another, as she sees how May, with all her difficulties, is loved and accepted by her sisters, and how June, who is a very prickly sort of woman, is loved and accepted. This allows her to accept her mother and to accept herself. She gains insight into her previous ideas about race, which allows her to grow into a person without prejudice. She also gains some insight into T-Ray, and this is important because Lily really needs that in order to move on, to not be crippled by a hatred of him. She falls in love, which is an important part of growing, and in this case, also helps her to grow as a human being without prejudices. She is exposed, for what appears to be the first time, to spirituality, in the form of Black Mary, which helps her to understand that there is a power larger than she, which also helps her to gain acceptance of herself and others.
The Secret Life of Bees is a fine example of the literary tradition of the "quest." Lily begins with a great deal of neediness, guilt, resentment, and heedless prejudice, and by the end of the book, she has gained an understanding of herself and the world around her that will allow her to continue to grow and thrive. I do wish Sue Monk Kidd would write a sequel because I think we would all love to know what happens to Lily now.