I don’t think we should expect to see them, though, because they are probably very far away in time and/or space.

Also the concept of a winning lottery ticket would seem to require the existence of a lottery game, which would seem to require some sort of society to play it. We are probably not the minimal working example of a society that is able to invent a lottery, but I bet that society is closer to us in complexity than it is to a scrap of paper.