Why does Jackson set the story at this time of year in "The Lottery"
Jackson set the story in June in part to establish the positive mood that permeates the setting in time and place, which helps to mask the horrific ending:
The morning of June 27th was clear and sunny, with the fresh warmth of a full summer day; the flowers were blooming profusely and the grass was richly green.
These positive, pastoral images of growth lead the unsuspecting reader into a simple agricultural community of uncomplicated farmers and their wives who--on a day like this--can only be celebrating life. And there is no foreshadowing here. The setting's literal goodness must be taken at face value.
June, however, evolves into its sinister reality, crushing the earlier mood, when Old Man Warner, the only citizen who can vaguely recall some of the ritual behind the lottery, remarks that
Used to be a saying about 'Lottery in June, corn be heavy in June.'
By this point, Jackson has provided sufficient foreshadowing to create some uneasiness, but Warner's comment here makes the connection explicit between the lottery and some sort of fertility ritual.
June, then, provides both misdirection in the form of agricultural innocence and a direct link between the horrific purpose of the lottery, fertility of the land.
Shirley Jackson's story "The Lottery" is reminiscent of the old Jewish tradition on Yom Kippur involving the sending of a goat into the wilderness after the rabbi has symbolically laid the sins of the people on its head. But, in Jackson's narrative, a scapegoat is traditionally made of a person in the superstitious hope that the planting in June will yield a good harvest. This practice is indicated as the townspeople stand around waiting for everyone to draw their lots as they do each June 27th. This date may reflect the period between the new and full moon (first and second quarters) as it is considered the best time to perform tasks which require strength, fertility and growth. As a certain Mr. Adams turns to Old Man Warner, saying some communities are doing away with their annual lottery, the older man snorts,
"Pack of crazy fools,....Listening to the young folks, nothing's good enough for them...There's always been a lottery...."
Mr. Warner is representative of those who blindly follow traditions and rituals regardless of whether they are worthwhile or not. It is also ironic that just as there is the beginning of new growth of crops, the community sadistically engages in the stoning of one of its members.