The traditions in A Rose for Emily are defined by the customs of the Old South. Miss Emily's father was controlling, dominating and in complete control of her life. Her existence is guided by a belief system and culture that was dying. However, her father, of the old guard, would never surrender his southern honor by allowing his daughter to marry someone he considered unworthy. So in view of this tradition, Emily's life is sacrificed. Although she lives, she has no life to speak of, except the brief time she has with Homer Barron, the man she poisons.
Comparatively speaking, there is a similarity in The Lottery, in that Tessie Hutchinson, a random victim, her life is sacrificed against her will also. She is a victim of a cruel and outdated tradition, like Emily, and has no power to stop the events that determine her fate.
Both stories highlight the tragic effects of outdated traditions that remain dominant in societies way beyond their significance or value. Clearly in Emily's case, she was a victim of the dying South. Tessie Hutchinson, in The Lottery, is a victim of a lottery system that chooses a random victim for an annual stoning to death. No one can remember why this annual ritual takes place, but they are afraid to abandon it.
Both the Old South and the village in The Lottery are male dominated societies. The actions of the men in these stories is not questioned.
Perhaps you can examine the traditions of subjugation of women and the potential for cruelty when the individual submits to the tyranny of what is socially acceptable in her lfie. For instance, Emily is a product of the Old South, a culture which has kept her from belonging to the community. Becaise she has been so isolated, she has missed the opportunity to have a normal relationship with men. So, she reacts in a grotesque manner when she does have a man. As in the actions of the community in "The Lottery" who converse with one another and are friendly prior to the selections, there is an incongruous union of decency and evil as they stone Tessie Hutchinson just as in Emily's actions toward Homer Barron.