I don't believe it is certain that this story takes place in New England. It might have been somewhere in the Midwest. Old Man Warner cites an old saying:
"Used to be a saying about 'Lottery in June, corn be heavy soon.'"
This seems to suggest that the story takes place in an area where the economy depends heavily on the corn crop and that the lottery represents a human sacrifice to appease some god or goddess of agriculture. New England is not known as a great producer of corn. The place sounds more like the Corn Belt, stretching from eastern Nebraska, through Iowa and into southern Illinois.
Shirley Jackson wanted to have a setting which was isolated and remote from the rest of America. It was only in such a setting that people could be stoning one of their neighbors to death every year without other Americans knowing anything about these events. And it was only in such a setting--a sort of Never-Never Land--that the people would be so ignorant and superstitious,
I have read that there was a big uproar when The New Yorker published "The Lottery" back in 1948. I believe a lot of people in the Midwest thought they were being targeted and insulted. The editor of The New Yorker, Harold Ross, couldn't have care much about what people in the Corn Belt thought, since he had few readers in that part of the country. James Thurber wrote a very interesting book about the funny, eccentric Harold Ross which is titled The Years with Ross (http://www.enotes.com/topics/years-with-ross). A New Yorker magazine cover, which has since been sold by the thousands as posters, shows a Manhattan dweller's mental picture of America. The surrealistic artwork is by the famous cartoonist Saul Steinberg. There is virtually nothing but wasteland west of the Hudson River.