Death is represented differently in the following three literary works: Macbeth by William Shakespeare, "The Sniper" by Liam O’Flaherty, and "The Lottery" by Shirley Jackson. How is it represented in each and why is it important? Please respond in a long essay, using specific evidence from the literary works.

I am not allowed to craft an essay for you; however, I can help you get started in the right direction. The first thing that you have to do is create a viable thesis statement. Most papers that ask for some kind of literature examination are asking the student to make some kind of argument about the piece or pieces and prove it through textual evidence. The writing prompt that you have been given appears to be steering you toward an essay that contrasts the three different literary works. That should be quite possible based on those three works. Since the essay is likely going to contrast the three works, I would use a two-sided thesis statement. The following is an example of something that you might consider using.
"Although Macbeth, 'The Sniper,' and 'The Lottery' all thematically feature death as a main theme, each story is unique in what it shows readers about death."
If the above thesis (or something similar) is your working thesis, then I would recommend the first supporting paragraph explain to readers how each story features death. The thesis statement claims all three pieces are thematically similar in that regard, so you need to prove to your reader that that is actually the case.
After that comparison paragraph, move into the breakdown of the individual literary works. Use at least one paragraph per piece. The goal is to show readers how each piece is unique and distinct in its representation of death. The order that you discuss each story in does not matter. For Macbeth, I would focus on how the deaths are mainly a result of murder. There are a few deaths that result from combat, but I believe those are secondary in importance for the play. For Macbeth and Lady Macbeth, murder is a means to an end. They both let uncontrolled ambition overpower any kind of moral compass that they each have. You might consider how Lady Macbeth and Macbeth react differently to the murders. For Macbeth, the first murder is the hardest. After Duncan's death, audiences never see Macbeth morally struggle as much as he did over killing his king. On the other hand, Lady Macbeth falls deeper and deeper into guilty despair over Duncan's death and the increasing body count. Using death as a means to an end isn't only confined to Macbeth. Killing Macbeth is used to set the kingdom back on the right path.
"The Sniper" has a different usage and representation of death. The deaths that the reader sees are a result of wartime combat. The sniper kills his targets because he is at war with an enemy, but he also kills his targets in order to save his own life. He can't have any of the three characters report his position. That would spell certain death for him.

Morning must not find him wounded on the roof. The enemy on the opposite roof covered his escape. He must kill that enemy and he could not use his rifle.

While the death of the other characters is a means to an end (he can escape), the killings are not premeditated like they are in Macbeth. The sniper is in the middle of a civil war, and it would be unfair to accuse him of murder like you could Macbeth.
In my opinion, "The Lottery" is the hardest of the stories to come to terms with. Combat killing is one thing. A corrupt character who murders is a different thing, but both possess motivations that can be understood by readers. "The Lottery" presents readers with a death that simply shouldn't make sense to us. Tessie is stoned to death by a mob of people doing nothing more than following a tradition that at least some of them question the appropriateness of.

"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."

Tessie's death just shouldn't happen. Surely the wisdom of the group will see error in stoning somebody to death for picking the wrong item out of a box. That doesn't happen, and Tessie is killed in order to show readers the dangers of blindly following tradition for the sake of tradition. I think "The Lottery," more than the other stories, has the power to make readers do a serious self-examination. We can comfort ourselves by knowing we don't have to kill because we are not in combat, and we can assure ourselves that we would never be so morally corrupt as to commit murder; however, we do seriously wonder if we would give in to the mob mentality that "The Lottery" shows us.