There are 6 US Post Offices in Lake County serving a total of 11,215 residents equating to 1,869 residents per post office. It's estimated that approximately 17,900 packages are handled across the 6 county post offices annually. Lake County is a county located in the U.S. state of South Dakota. As of the 2010 census, the population was 11,200. Its county seat is Madison. The county was formed in 1873."