Great question! Although Old Man Warner is just a minor character in this masterful short story, it is well worth thinking about how he is used by Jackson to support one of the central themes in the story, which is how we can continue to be involved in unjust and horrific practices because of tradition. Note how throughout the story Old Man Warner speaks up for tradition - we are told that he is the oldest man in town and that he says during the lottery that it is the "seventy-seventh year" he has been in the lottery and he also has some harsh words about those communities that have given up the lottery:
Old Man Warner snorted. "Pack of crazy fools," he said. "Listening to the young folks, nothing's good enough for them. Next thing you know, they'll be wanting to go back to living in caves, nobody work any more, live that way for a while. Used to be a saying about 'Lottery in June, corn be heavy soon.' First think you know, we'd all be eating stewed chickweed and acorns. There's always been a lottery," he added petulantly.
Note how this important speech ties in explicitly with some of the central themes of the novel. Old Man Warner's approach is that tradition must be right because it has been practised for so long. To try and change it would be, in his eyes, as stupid as going back to living in caves. The idea of change is impossible to him. Note, too, how at the end he plays a key role in encouraging everyone to finish off the Lottery.
Therefore in this short story Old Man Warner plays the role of speaking up for tradition and how difficult it is to change tradition, even when it causes us to commit terrible crimes that we can often be blind to.