In Shirley Jackson's short story "The Lottery," the lottery takes place each year after school has been let out for the summer. The omniscient narrator tells the reader that the lottery takes place on June 27. It is noted that in other towns that are much larger, it must be started the day before so as to end on the 27th.

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.

This kind of description sets the mood based upon a pleasant and beautiful day, when life abounds in the descriptions of nature. The story's themes are in dark contrast to the description of this lovely scene. 

[T]he story takes place on June 27, near the summer solstice, one of the two days in a year when the earth is farthest from the sun. 

Upon closer reading, tying the date to the summer solstice may engender a sense of an uncivilized yearly ritual; we might also imagine that being so far from the sun, it would be a time associated with death. The sun is the source of life on our planet. Being so distanced from the sun might infer that the world is colder towards its inhabitants—paradoxically, rather than being drawn closer to this source of life, we are distanced from it and all the life-giving properties associated with it.

The official date for the annual lottery was June 27th. More populous villages start the ceremony a few days earlier so the climax coincides with the official date. The village in the center of the story starts the lottery on the official date because there are fewer participants compared to other villages. The event in that village only takes two hours to complete. The lottery commences at ten in the morning and finishes in time for lunch.

The lottery is held in the village square. The children arrive first, and they are in charge of collecting the stones. They are followed by their fathers, who congregate around the square and talk among themselves. The women arrive last and join their husbands in the square.

Which day does the lottery fall on in Shirley Jackson's "The Lottery"?

The lottery took place on June 27th in the village square. In more populous villages, the lottery took longer to conduct and started two days before the official date. The village in the center of the story only had a population of 300 people, and the lottery took less than two hours to conduct. The people gathered in the square from 10 o’clock in the morning. The children, who were on school break, assembled first. They played around the square, talked about their teachers and books, and made a pile of stones in one corner of the square. Men gathered next, and they talked about farming and taxes. The women were last to assemble. They briefly talked to each other and proceeded to join their husbands in the square.