There are several incidents that show conflict in the story.
There is the conflict between the judge, his conscience and the entire mood in the courthouse. The judge wanted to deliver justice but the mood in the court suggested otherwise. The people are not concerned with justice since all they are seeking is to punish Laura for beating up and embarrassing Mr. Beasley. At one point the judge was even forced to convince Laura to give her testimony:
Believe it or not, Laura Lee, this is a court of law. It is needful to hear both sides of every question before the court can reach a conclusion and know what to do.
There is the conflict between Laura and Mr. Beasley; she was loyal to her employer and this forced her to attack Mr. Beasley who was taking advantage of the situation and in reality attempted to steal Mrs. Celestine’s belongings. The conflict between the two is aggravated further when Beasley lies in court about the value of the items he wanted to take against his loan.