In the story, the Quakers not only belong to a religious order, but members of the sect are also Lyddie's neighbors. For example, Quaker Stevens owns a farm near Lyddie's family's property.
In Chapter Two, Lyddie and Charles are being sent to work as a miller's helper and a housemaid respectively so that they can help to pay off their father's debts. Before they leave, they have to take the horse and cow to a Mr. Westcott to pay off a debt they owe him. Lyddie and Charles hope to sell their calf to Quaker Stevens for a good price.
Even though Quakers as a rule are expected to live simply, Lyddie notices that the Stevens farm is a substantial one. The farmer is kind to the children and buys the calf for twenty five dollars. Then, he invites them in for the noon-day meal. Both children notice that the kitchen itself is larger than their whole cabin and shed thrown together. The meal is lavish in the children's estimation, and the Stevens family is wealthy enough to own its own loom.
In the early chapters of the story, it is Quaker Stevens who lends his bull to the family as a favor: the bull mates with the Worthen cow, and each spring, calves are born and then sold for money. This is partly how Lyddie, her brother, and their mother survive after Lyddie's father leaves the family.
So, in the story, the Quakers are Lyddie and Charles' neighbors. They are kind, compassionate, and loving people who do the best they can to help Lyddie and her family, despite Lyddie's mother's suspicion of Quakers as "heathens" and "abolitionists." Later, Luke Stevens (the youngest son) asks Lyddie to marry him, but she decides to attend college instead. The novel ends ambiguously, and we are left to wonder if Lyddie will later accept Luke's suit.