(answer to the question "Can lottery replace/complement democracy?")
Your concept sounds close to Athenian democracy, but it would be much more complex nowadays. A parliament is made of lawmakers and lawmakers are coping with a very complex system of laws, impacts, lobbies... The people need to know their MPs better than they would know candidates in a reality TV show. Not all politicians are crooked or evil, and democracies work because of the expertise of great lawmakers. Besides, I don't want the future of my country to be sponsored by Ladbrokes or betwin.com. As a parallel reality show to contribute to the education of the masses maybe, but not as the main dish, and even that show could turn into a dangerous joke, making people less interested in actual politics, more boring and less demagogical.
In the Middle Age, some cities used to treat a fool as their king or their bishop for one day, but the joke was on him ("Fete des fous" or "Fools Fete / Party", not to be confused with April Fools' Day).
During the French elections, Segolene Royal, the Socialist candidate, suggested to have a group of voters randomly selected to keep an eye on their MPs, mayors... which any citizen has already a right if not a duty to do in a democracy. So the joke was on "Demagolene".