In order to win the lottery you have to buy a ticket. Not everybody wins, but that man can make a difference (or not ) in this world. We all have a shot at the BIG prize.
The author acknowledges this and isn't arguing about whether the lottery exists, but what the stakes are. For the working class, they stake their livelihood. It means that failing to win the lottery might mean starting a career from scratch, that is, if they enough to still have roof and food.