In a story this sparse, it's pretty striking how much the boys of the village tell us, not only about the nature of the lottery (consider that early, ominous pile of stones), but also about the raw feeling underlying this village ritual.
Summer vacation has just begun:
[...] the feeling of liberty [sits] uneasily on most of [the village's children]... their talk [is] still of the classroom and the teacher, of books and reprimands. (2)
So, there's liberty, the natural state of children—and then there's school, which reins in their behavior (i.e., those reprimands referenced by the narrator). On this fine June day, though, school's out and stones are in: we're leaving behind everything that school represents (e.g., civilization, law) to access that "liberty" that the boys in the story are beginning to enjoy so much.
What evidence do we have that the village boys are really getting into this village ritual? Well, there's the first sentence of the second paragraph:
The children assembled first, of course. (2)
They're too excited to wait. What's more, Bobby Martin, Bobby and Harry Jones, and Dickie Delacroix have already begun collecting stones (we don't initially know why). When they're called to order so that the fateful drawing can begin, the boys heed their parents reluctantly,
[...] having to be called four or five times. (3)
And that little scamp, Bobby Martin,
[...] [runs], laughing, back to the pile of stones. (3)
The boys get that the lottery's trappings of tradition—the black box, the strips of paper, all that bit—are a pretext for the really important part: the stoning.
That pile of stones right at the beginning reappears as Tess's fate is decided. Jackson explicitly connects the boys' behavior to the adults' murderous desires:
Although the villagers had forgotten the ritual and lost the original black box, they still remembered to use stones. The pile of stones the boys had made earlier was ready. (76)
There's a lot in this story about how tradition authorizes community violence, but Jackson's also throwing in her two cents about the essentially brutal nature of human beings. These kids embrace what their parents have to hide under a decorous lottery draw: they are looking forward to killing someone. Those rocks they collect stand as terrible proof that this group of regular children wants to murder someone "in time for lunch" (1).
In fact, all of the villagers seem pretty eager, but the boys are the most forthright about it.
We also want to comment on why we're specifying "The Boys" and not "The Children"; after all, the girls are also gathering early for the event. But it's not the girls who are collecting stones. They're:
[...] [standing] aside, talking among themselves, looking over their shoulders. (2)
Why does Jackson distinguish between boys and girls in their anticipation for the lottery? We think it has a lot to do with the fact that it's the men of the family who must draw the first lottery strips. According to ritual, it's the males of the village who bring their wives and children into the running for the lottery; they take the initial risk, and their sons seem to enjoy it the most.
Jackson is playing on stereotypes of masculine violence—but she's also undercutting ideals of "feminine" peace with the brutal characters of Mrs. Hutchinson and Mrs. Delacroix. The men in the village aren't the only ones enthusiastically participating in this ritual murder. It's just that the little boys are the ones that really seem eager for the carnage.