The black box represents death of the people of the town. Those who have died, and those who will be chosen next and die in the future.
Figure of Speech: Forshadowing
The black dot on the paper means that either your family was choosen from the first drawing, or you were choosen from the second drawing. When you see the black dot you immediatly probably feel scared because you know you're going to die.
The men drawingo for their families represents how traditional and old fashion the town is. The town is still stuck with misognistic values. This leaves clues that the story either takes place in the past or into the future.
"Bobby Martin had already stuffed his pockets full of stones" The fact that the author includes stones so much in the beginning of the story made me believe that if you won the lottery, you don't get money, you get stoned.
"The morning of June 27th was clear and sunny, with the fresh warmth of a full-summer day; the flowers were blossoming profusely and the grass was richly green."