Lula is a member of Calpurnia’s church who hassles her for bringing the Finch children to services.
Lula and Calpurnia do not get along. This is clear by Calpurnia’s reaction to Lula when she brings the Finch children to her Negro church, First Purchase.
I felt Calpurnia's hand dig into my shoulder. "What you want, Lula?" she asked, in tones I had never heard her use. She spoke quietly, contemptuously. (ch 12)
Scout also notices that Calpurnia talks like Lula and the rest of the blacks attending the church, rather than the way she talks around the Finch children.
Lula complains that the white children do not belong at the black church, and they are not Calpurnia’s company, because Calpurnia is not their company when she is at their house. They are employers, and should not be encroaching on the black services, from Lula’s point of view. Calpurnia responds that, "It's the same God, ain't it?" (ch 12), and the children stay.
Zeebo, Cal’s son, tells the Finch children not to worry about Lula because she is a “troublemaker” who has “fancy ideas an' haughty ways” (ch 12). The children are surprised to see that most of the people in the church cannot read, and the church has very few hymn books.
These days, we would refer to what Lula is doing as "reverse discrimination." However, Lula's point of view is also understandable. She felt that her time was being encroached upon by the white children of the people who treated her so badly. It is yet another example of how deep the divide is and how thick the tension is between the races in Maycomb.