The point of view of a story can be identified by considering who is telling the story. Is it a person who is part of the narrative? Is it the protagonist of the story, telling the events of the narrative in the first person, with words like "I" and "me"? Or is it written in the third person, with words like "they"? And how much does the narrator know?

In this case, the story is being written in the third person. We can see that the narrative voice does not use "I" statements; it isn't telling us about events which the narrator seems to have personally had a part in. On the contrary, the narrative voice seems to replicate that of a documentary, particularly given that it begins very exactly with the date "June 27th."

Note the use of the distancing term "the villagers" to describe the people in the story. This is a strong indication that the narrator is not one of these people. However, at the same time, the narrator is aware of what the villagers think and feel, albeit in broad strokes, rather than individually. The narrative voice knows where the box is put over the course of the year, and knows how the villagers feel not only about the box and the tradition, but also about the other villagers.

This general air of knowing everything about everyone in a narrative voice is normally described as omniscient narrating, or all-seeing narration. The narrative voice of this story, then, is third-person omniscient.

The point of view employed by "The Lottery" is third-person omniscient. At first, the narrator only describes what is immediately observable: that people are gathering together, that the men smile rather than laugh, that the women call out to their children. A third-person objective narrator cannot report any characters' thoughts and feelings, and a limited omniscient narrator can report only one character's thoughts and feelings.

However, the narrator soon begins to describe the thoughts and feelings of multiple characters, something only an omniscient narrator can do. First, the narrator describes Mr. Summers as a "jovial man" who has "time and energy to devote to civic activities." These are not immediately observable and require some intimate knowledge of his thoughts and feelings in order to ascertain. Further, "people were sorry for him, because he had no children and his wife was a scold." The statement that people feel sympathetically toward Mr. Summers is a description of how they think, not something they say aloud during the course of the story.

Moreover, the narrator tells us that "no one [in the village] liked to upset even as much tradition as was represented by the black box" used in the lottery. Again, this is not dialogue but, rather, a description of the villagers' internal thoughts and feelings. It is information like this that helps us to ascertain that the third-person narrator is omniscient rather than objective (not reporting anyone's thoughts and feelings) or limited omniscient (only reporting one character's thoughts and feelings).

The point of view of "The Lottery" is the third person point of view.  

A third person point of view places the narrator outside of the events happening in the story.  The narrator obviously knows characters and things that are happening, but a third person narrator means that the story's narrator is not a character within the story.  More specifically, the narrator of "The Lottery" is narrating from the third person objective point of view.  This allows the narrator to jump from person to person and group to group.  Readers are allowed to listen in on various conversations as if we are eavesdropping on everybody.  

The fact that the narrator is only capable of eavesdropping on people is why this story's point of view is third person objective and not third person omniscient.  An omniscient narrator is privy to the internal thoughts of characters, and the narrator of "The Lottery" never indicates that knowledge. That's a good thing for this story too.  If readers knew the thoughts of the characters, the final shocking moments of the story wouldn't be as shocking.  

One natural effect of the third person narration is that readers feel a bit of distance from the events happening in the story.  We feel invested to a certain extent, but we also know that the events (good or bad) are always happening to somebody else.  That distance is important for this story.  While readers are appalled at the realistic feel of the lottery, we can at least take comfort that the people are not our personal friends.  It's not my town's tradition.  It's their town's tradition.  I've often wondered what this story might be like from the first person perspective.  I don't think the ending would be as shocking, because a character narrator would likely give away his/her apprehension about the lottery system.