The two stories are similar in that they talk about two societies, two discreet groups of people. These are unusual stories because they do not involve the choices and actions of certain individual characters; they involve the choices and actions of the societies as a whole. Identifiable characters are not important to the stories, for all the people in each story act in concert.
So, instead of characters making choices, the societies make choices, and the choices the two societies make in "The Lottery," and in "The Ones Who Walk Away From Omelas" are similar in that they involve a single, agreed-upon act of cruelty. This act of cruelty is a long-held understanding and tradition that helps define the society and keeps it intact. In "The Lottery," the tradition is the yearly, random stoning to death of a single member. In "The Ones Who Walk Away From Omelas," it is the despicable, continual degradation of a single, abject member of the society.
Both societies are cruel; it is only the manner of the cruelty that makes them different.
When writing a comparative essay on two stories, it is often helpful to spend time in reflection before writing. For instance, ask what commonalities exist between the two stories. That is, what themes/moral truths are similar? Are there any characters who are similar? What similarities exist between methods of narration?
In addition to the already mentioned questions, in the examination of "The Lottery" and "The Ones Who Walk Away from Omelas," the writer may also wish to do some research on these stories. For instance, Shirley Jackson's story has as it basis the ancient concept of the "scapegoat" while LeGuin's story takes William James's theory of pragmatism, what is best for the majority to its moral conclusion. This theory also states that a person's thoughts should guide his or her actions, and truth is a consequences of a person's belief. So, in a sense, some of the people in Omelas who accept the state of contentment in served by the one creature accept also the scapegoat concept.
LeGuin's intrusive narrator forces the reader to reach a moral conclusion as well, while the narrator of "The Lottery" gives no indication of what is to come. Instead, this neutral narrator surprises the reader into drawing his/her own conclusions at the end of the story, one conclusion being that of the innate penchant for violence in people.
Indeed, there are similarities between the stories, yet some differences exist. A comparative essay discusses both. So, write down ideas and find a thread of an idea to hold everything together--themes may be such a thread. Certainly, there is much to write about.
Check out the site below as it will help you in organizing your essay. (The alternate pattern is preferred by professors for essays of this kind. See #3 of Writing a Compare/Contrast Essay)