Situational irony is a literary device used by authors to produce an incongruity between what the reader expects will happen in the story and what actually takes place. Something surprising will occur that nobody sees coming. The reason why authors employ situational irony is to cause the audience to take a second look at the details in the story, so that they can make comparisons of what they though was real, and what was actually their own imagination.
In "A Rose for Emily", the situational irony is that, at all times, the reader assumes that this is the story about a woman of a genteel heritage who has turned erratic and unable to catch up with the present world. The whole time, the townsfolk narrator maintains a tone of condescension, in hopes of helping the reader understand that "Miss Emily" is not a bad lady; she is the victim of her overwhelming family, which was so stuck up and bent on acting better than everyone else.
What nobody expects, and seemingly neither does the narrator, is that, after Miss Emily's death, the neighbors curiously look around this house which had been locked to the world for decades. This is when they find the carcass of a man laying on the bed that Emily, even shortly before her death, was still using. Emily slept with the man that she killed, for years.
In "The Lottery" the situational irony, which permeates the story, begins on an idyllic day. The town is out and about, and people are getting ready for "an event" where everyone gets to participate. The kids are playing, the sun is out. It looks like a regular day, after church, with everyone sharing in communion.
The morning of June 27th was clear and sunny, with the fresh warmth of a full-summer day; the flowers were blossoming profusely and the grass was richly green.
The event to take place, the lottery, sounds innocent enough. We have all participated in some kind of lottery. The name of this game of chance elicits thoughts of surprise, winning, hoping to win, and maybe even getting the proverbial "bragging rights".
In some towns there were so many people that the lottery took two days and had to be started on June 20th, but in this village, where there were only about three hundred people, the whole lottery took less than two hours, so [...] the villagers [can] get home for noon dinner.
Fair enough. This villagers' game, called "the lottery", is permissive enough to allow for dinner time at noon. It is traditional enough to be celebrated in a consistent basis. It is also important enough that nobody can miss it.
What we do not realize, as readers, until the end of the story, is that this lottery was celebrated for centuries, for reasons that not one villager can fully explain nowadays, and that the purpose was to kill the villager whose name came up from a pool of names that everyone was obligated to submit.
More ironic still is that, when Ms. Hutchinson's turn came to be stoned to death, her neighbors carried on like usual, carrying big stones to finish her on the spot so that everyone can "go back to normal".
Therefore, the irony on both stories is that they show what seem to be normal situations, stamps of everyday life, not telling the audience that, beneath the surface of calmness of what is expected to be "normal", lurk monsters created by us, which make us destroy one another.