Cultural literary criticism takes the specific culture into account, making sure to analyze the cultural context of a story and the cultural implications of the story's theme or viewpoint. In "The Lottery" by Shirley Jackson, the story is set in a fictional but vague time and place, so no specifics are offered as to what country, region, or epoch is involved. This gives the work a feel of universality and it reads as a parable or allegory.
Allegory can include time and place, as in Animal Farm, which is clearly about post-World War II Russia, but often it simply uses oblique references to time (as in The Alchemist by Coelho or The Pearl by Steinbeck) while setting a general scene within a specific physical environment.
Since "The Lottery" is an allegory, it is up to the reader to extrapolate the culture from clues. Although the story happens in a village, the modern American reader will have the impression it takes place in modern, post-industrial times. There is zero information to support that, however, except the author is a contemporary (midcentury) American.
From a cultural criticism standpoint, "The Lottery" eviscerates human behavior, rather than a particular culture. Many cultures have used sacrifice; ancient cultures sacrificed both war captives and citizens while modern cultures use a military draft.
By the same token, the country in which The Village lies is not made explicit. But we assume it is an American country, perhaps a European one.
The point of "The Lottery" is that group/societal rituals are necessary for the benefit of the whole. The brutality of a universal lottery, in which one person—adult or child—will become the sacrificial lamb is juxtaposed with an implicit modernism.
"The Lottery" is horrifying because it could be happening today, in your town. The lack of detail makes the possibility of such a lottery real. The lack of cultural context makes the story more relevant, so that it subsumes all cultures in its telling.
For the sake of comparison, the novel The Hunger Games also employs a lottery; however, its lottery takes place in a dystopian future. The reader doesn't feel immediately threatened in The Hunger Games because its culture is distant, fictional, and specific.