The Lottery and their crops growing, well is probably just a coincidence. But if you do a ritual for so long and the coincidence is right, then the townsfolk are lead to believe in this the truth.It is also interesting that old man Warner says that the other towns are dumb for stopping the lottery.What we don't know is whether or not that it had any impact on their crops.
I can only assume that the Lottery box is a symbol for Death and that Black Spot