There is no real parent lottery. Randy Pausch used the phrase "parent lottery" as a way of expressing his luck in having the parents he had. Pausch considered that many of the experiences he had and the lessons he learned from his parents were central to allowing him to take advantage of the opportunities that became available to him later in his life.
They allowed him to be himself, to paint a submarine and an elevator on his bedroom walls. They taught him to care about others and to get involved in doing so. They encouraged him and refused to allow him to give up on himself and his dreams. Pausch felt he won the "parent lottery" because he had the great good fortune to achieve his life's dreams thanks to their foundational influence in his life.