Keep in mind that Lucy Ann Potts is Zora Neale Hurston's mother, so her inspiration is pivotal in Dust Tracks on a Road. In reality, the character of Lucy Ann Potts reverberates throughout Zora's entire autobiography (from Zora's youth to her move to California) in that she keeps the family together through matriarchal love and optimism.
Even before Zora is born, Lucy Ann Potts makes a big, strong decision by marrying a young black man without much money, but with lots of potential. Even though Lucy was raised in Georgia, she takes a chance by moving to what will become Eatonville, Florida with the man who will become her husband. Consequently (and with Lucy's help), he becomes the mayor of Eatonville as well as the pastor of the Baptist Church there. (Fans of Zora will definitely connect Lucy and her husband with Janie and Joe Starks of Zora's Their Eyes Were Watching God.) It is in Eatonville where Zora is born.
In Zora's youth, her mom is the voice of optimism and educational encouragement. Those are the two ways that Lucy Ann Potts always "keeps the family together" which is the root of your question. Lucy always encouraged her daughter to "jump at de sun" and continue with her educational goals. It was also during this time that Lucy Ann Potts became the matriarch of the family, encouraging others to achieve their goals as well. This type of optimism would carry Zora through both her personal life as well as her professional life.
In conclusion, it's important for the reader to note the importance of Lucy Ann Potts' death in the life of young, nine-year-old Zora. It is a tragedy for Zora to lose both the voice of optimism as well as the matriarch of the family. As a result, Zora considers the death of her mother to be a turning point in her life that leads to Zora's own independence in addition to the beginning of her career as a writer.