The townsfolk in "The Lottery" appear to be pagans. In many ancient pagan societies, it was believed that in order to ensure the success of the harvest, sacrifices of one kind or another had to be made to the gods. Good harvests were essential for such communities; if they failed, widespread starvation could ensue. So it was considered absolutely crucial to do whatever was necessary to appease the gods, even if it meant resorting to human sacrifice.
And that's what happens in "The Lottery." The annual lottery is held in June to make sure that once the human sacrifice has been made, a bumper harvest will inevitably follow. That's what the old man means by "Lottery in June, corn be heavy soon." What makes the annual ritual sacrifice especially disturbing is that it takes place in a modern town. Indeed, it is ironic that the townsfolk feel the need to resort to such primitive rites in order to maintain a modern standard of living. They firmly believe that if human sacrifices aren't made every year, then the crops will fail, and if the crops fail then the community will be forced to revert back to a more primitive standard of life.