"By lot" means that Athens citizens (white males over the age of fifteen) put their name on a stick of wax and put it a container and someones drew out some of the sticks, or drew "lots." And sorry for the short answer.
When we hear that the Council of 500 was chosen "by lot," what this means is that the council was chosen at random. All the candidates would put their names together and it was luck that decided who was going to be in the council. This was probably not a very good idea for the Athenian goverment, as it was likely that the people elected to the council were uneducated or uninterested in government.
