In To Kill a Mockingbird what is the purpose of the scene between Cal and Lula at First Purchase?
This scene serves a couple very useful purposes in showing the cultural and societal conflicts that existed in the South during the time that the novel is set. Even though it is a very simple scene--Lula confronts Cal about bringing white kids to church, and is quietly put in her place--it actually is layered with deep meaning and significance.
First of all, it shows the attitude that some black people had at that time, which was one of isolation and anger at the white culture that was repressing and discriminating against them at the time. Lula felt that the black people should keep themselves separate and not condescend to work for white people as lowly servants. She had too much pride for that, and a more segregationist attitude, she felt, would serve her people well. Don't mix with the whites in any way, shape or form.
Secondly, it reflects the attitude that the white people that employed many of the attendees of the First Purchase church did not belong in their private lives. The church was one place where they could be themselves and not worry about being fired or judged by white people. It was a place to relax, to be at ease and comfortable in their own skins. If white people were in attendance, then they would not be able to do that as much. It shows how they often were stiffer, more careful versions of themselves around white people, and how it was nice to take a break from that sometimes.
Another layer in this episode is that is relays important information about Calpurnia to Scout. Scout is shocked that Cal would speak and act differently than at their house, and at the realization that Cal actually has a life outside the one she has seen her in. This is an important realization for Scout in her coming-of-age story. She needs to realize that the lives that black people truly led were in actuality very different than she realized.
Lastly, this story goes to show how much Cal loved Scout and Jem. She stands up for them and is willing to risk the ire of some of her people by bringing them to the church. Also, it shows how most of the people she lived with were kind and accepting, no matter the skin color. Lula was an extreme fringe, whereas most of the people there were unbiased and loving towards all people, white or black.
I hope that helps; good luck!