There are many conflicts in the short story. What makes these conflicts so powerful is that they are underneath the narrative. In other words, the conflicts are unspoken. This makes sense, because the story is about the ritualistic murder of a person. The townspeople do it not because they want to but because they have to. More to the point, the story is about the ritualistic murder of a member of your society. So, it is possible that you had that person over for dinner the night before.
In light of this plot, we can immediately see the moral conflict. The people will have to kill someone they know. All feel uncomfortable with this act, but they do it any way, because tradition holds sway. Moreover, it is clear that Tessie, who is chosen at the end of the story, does not want to accept her lot. Hence, there is conflict.
Physical and emotional conflict also exists. The physical conflict comes into play in at least two ways. First, someone in stoned to death. Hence, there is brutality, even if it “off screen.” Second, the rest of the townspeople do the stoning. What make this even worse is that the children are involved. At the beginning of the story it says:
“Bobby Martin had already stuffed his pockets full of stones, and the other boys soon followed his example, selecting the smoothest and roundest stones…”
In light of this, it is no wonder that some villages contemplate the giving up of this practice. The text says:
"They do say," Mr. Adams said to Old Man Warner, who stood next to him, "that over in the north village they're talking of giving up the lottery."
This shows that people know deep within that this practice is wrong. The sad point of the story is that in the end, nothing changes.