Well, strictly speaking, "The Lottery" is written using the omniscient point of view. It is not written using the first person point of view, and whilst it is written using the third person, it does not follow the action from the perspective of one character. The issue, however, is that Jackson as the omniscient narrator chooses to restrict the amount of information that we are given. Of course the characters all know what is going on, but crucially we as readers do not, and it is only in the final paragraphs that we understand what this Lottery is all about and what the tragic conclusion of it is. For Jackson to have given us access into the minds of the characters would have destroyed this massive sense of shock that we are provided with and made all the subtle elements of foreshadowing that she gives us (like the boys collecting stones at the beginning) unnecessary.