Concerning Jackson's "The Lottery," I think the issue you're getting at is that no concrete reason for the existence of the lottery is given in the story. None of the characters seems to know or care why they participate in the lottery once a year. They seem to participate because it is a tradition, period; because it's what everybody does. That's the point.
Given the right (or wrong) circumstances, normal people are capable of atrocious acts. If you view this as a scapegoat story, otherwise normal people are capable of great cruelty to scapegoats. The fact that there is no logical reason for the lottery is the point.
I don't see any specific significance in the use of stones as opposed to any other method of execution. At least not as far as what you mention about the people remembering to use stones. If there's significance in the use of stoning, it's that it is biblical, ancient, and heinous.
The purpose of the lottery has not changed. A death needs to occur for their harvest to be successful. This implies that the people are stuck in their ways and do not question if there is another way for their harvest to be successful.
In the very beginning, the children are playing with the stones:
Bobby Martin has already stuffed his pockets full of stones, and the other boys soon followed his example, selecting the smoothest and roundest stones;
This understanding has obviously been handed down from generation to generation. Oftentimes, a new generation questions the older of a purpose. The answer here is always, "because that's how we do it."
Consider how many times in our culture that's been questioned. If we didn't question our rituals and normal routines, science and technology wouldn't have created near the amount of conveniences we have today.
That's an interesting question -- after all, what would a stoning be without stones...
But it brings up a good point. I think what it shows is that the people have some underlying desire to do violent things to one another.
If all traditions were honored equally, then nothing about the lottery should have changed. But many changes have actually been made. The fact that the stones keep being used shows that the people don't really care about things like what the names are written on. But they do want to keep on hurting others.
If this were not so, they could change and make the stoning symbolic by using rotten tomatoes or something.
So, they'll give up parts of the ritual, which means it is not JUST tradition that is driving them. But they won't give up stoning, which means they really want to do that part of the ritual (the violent part).