"The Lottery" is about capital-T Tradition, the kind of tradition that "no one liked to upset" (5). Given how symbolic the other characters are—Mr. Graves, we're looking at you—it's only right and proper that there be a character who stands in for tradition.
Jackson doesn't disappoint: there's Old Man Warner.
After all, the dude's first name appears to be "Old Man." Jackson is once again creating a figure who's not so much a real person as he is a stand-in for something else, in this case, those nostalgic days gone by. (And, once again, we can't ignore the literal meaning of his last name: Warner, one who warns.)
We learn that:
[...] the black box now resting on the stool had been put into use even before Old Man Warner, the oldest man in town, was born. (5)
In other words, Old Man Warner is a benchmark for tradition: if the box is older even than Warner, it (or at least, pieces of it) must date back to that hazy time when the lottery first began.
As the oldest man in the village, Old Man Warner seems to take it upon himself to make sure that the village doesn't change. When he hears that other towns have given up the lottery entirely, he grumbles,
"[...] used to be a saying about "Lottery in June, corn be heavy soon." First thing you know, we'd all be eating stewed chickweed and acorns." (33)
So, for Old Man Warner, the lottery is associated with agriculture and with plenty; it allows the community to guard against nameless, declining fortune. Old Man Warner is the one who comes the closest to stating a rationale for the lottery, which apparently has origins so old that even he can't say how it began; all he knows is that it is associated with abundance and with the cycle of the year.
This association of the lottery with nature is super-important, even beyond the hints it gives us about the history of this ritual. The thing is, we have no idea if what Old Man Warner's saying is anything close to true. But he ties nature to the lottery with complete ease; in other words, the tradition feels natural to the villagers. For the most part, they utterly fail to question the lottery because to do so would be like questioning why we live in communities with one another. It's that much a part of the yearly cycle of this village.
The antiquity of the ritual, its forgotten origins, and its ties (through Old Man Warner) with nature all point to a kind of mythic past for the ritual, before civilization. Without this ritual to guard the community, Old Man Warner fears scarcity of a specific kind: the village would go back to chickweed and acorns, the diet of a hunter-gatherer rather than a farmer.
The lottery could be a means of regulating and rationalizing the savagery that the boys of the town bring so close to the surface. It is the relic of a human transition from savage to "civilized man" – but the only difference between the two is that the "civilized man" dresses up his murderous rage in a black box and strips of paper before he lets himself loose.
Old Man Warner's assertion that "It's not the way it used to be [...] People ain't the way they used to be" (69) implies that Old Man Warner likes to reminisce about the good old days. Whether people "ain't the way they used to be" may or may not be true; all that matters is that, as the voice of tradition, Old Man Warner is fulfilling his role as a stereotype of the crotchety old man, resentful of newfangled ways, the lack of discipline among young people (as represented by Nancy Hutchinson's friends speaking out of turn at the end of the lottery), and, especially, the reform-minded "young Joe Summers" (33).
Interestingly, Old Man Warner provides an explanation for the lottery that nobody listens to. His pronouncements about why the lottery can't end don't ever provoke comment from the other community members. Tradition works in this story as a force beyond reason. The village doesn't need to hear why they must keep holding the lottery; it's enough that they know they have to—and really, secretly, they kind of like it.