Jackson seems to be implying that human nature often involves a kind of "herd mentality," in which people cease (or perhaps never begin) to think for themselves but are instead content to do things as things have always been done. She may also be suggesting that the need for communal rituals is very deeply implanted in human nature. It is also possible that she is implying that a yearning for violence is a deep-seated impulse in human beings -- that humans are innately capable of evil.
In regards to family loyalty she makes the point that it only goes so far, at least as seen through the behavior of Tessie. It is a fact of the lottery that married daughters are counted as part of the husband's family, but when the Hutchinson family is faced with the second draw, Tess wants to better the odds of her not being the one to be drawn by adding her own daughter to the mix of people who could face the stoning. Doesn't seem very motherly of her does it? It is a great example of self-preservation at any cost.
She's implying that tradition can lead to us doing stupid and even evil things and that our human nature is such that we just go along with the tradition. That's what's going on here, right? No one hardly even remembers why they do the lottery but they just keep doing it because it's tradition.