Harper Lee introduces the character of Lula in order to tell "the other side of the story," that there are tensions in the black community as well as in the white community. Lula represents those blacks who find the accusations against Tom Robinson very unfair--even offensive and malevolent, especially since they all know the Ewells who do not live far from the "black nest" as Bob Ewell calls it.

In Chapter 12 or To Kill a Mockingbird, despite some racial tensions because of the impending trial of Tom Robinson, Calpurnia brings Scout and Jem with her to her church on a Sunday that Atticus is gone. As they enter, the men remove their hats, and the women cross their arms before them in respectful postures.

But, suddenly out of nowhere, the children hear a voice, "What you up to, Miss Cal?" Her pose of a hand on one hip and palm of her other open in a point, indicates that she is not pleased. With Calpurnia's hand resting upon Scout's shoulder protectively, Calpurnia replies in "tones I had never heard her use," Scout remarks. In response to Lula's demand to know why Calpurnia has brought two white children to their church.

"They's my comp'ny," said Calpurnia. Again I thought her voice strange: she was talking like the rest of them.
"Yeah, an' I reckon you's comp'ny at the Finch house durin' the week."

Lula hostilely moves forward, but Calpurnia stops her abruptly, speaking in the vernacular.  Still, Lula is resentful, telling Calpurnia has no business in bringing white children to their church. But, Calpurnia replies wisely, "It's the same God, ain't it?"

In order to diffuse the situation, one of the male members of the church welcomes them.

I think Lula's character helps illustrate how much of a protective mother figure Cal is to the children. Notice how she fiercely protects the children when Lula questions her as to why she is bringing them to their church. This also foreshadows the racial tension that is building up because of the looming Robinson trial.

What the scene also does is to illustrate the ways in which the black community has been so segragated from the white community.  Calpurnia works amongst the Finches, and Jem and Scout have always accepted her as a part of their world.  But there are no other African-Americans that exist in their world.  This is because they have been pushed aside, out of sight if you will.  Lula is upset because the whites won't allow the blacks to be a part of their community - therefore, the whites shouldn't try to be a part of the black community.  It is a matter of pride - you don't want us, so we don't want you.  Of course, some of that will change with the trial, as Jem, Scout and Dill are permitted to sit with the negros in the balcony of the courthouse.

Lula is a black woman at Calpurnia's church who is indignant that Calpurnia has brought Jem and Scout to their Sunday service. She rudely says, "You ain't got no business bringing' white chillun here - they got their church, we got our'n" (Chapter 12).  Lula illustrates that prejudice and stereotyping is not something that is confined to one particular group, it is pretty much found everywhere. As a member of a racial group which has been discriminated against by white society, Lula turns around and gives the same unfair treatment right back to innocent individuals, solely because of their racial identity.  Lee appears to use Lula to show that, unfortunately, prejudice can and does work both ways.