Lake County is a county in the U.S. state of South Dakota. As of the 2020 census, the population was 11,059. Its county seat is Madison. The county was formed in 1873. The terrain of Lake County consists of rolling hills, with the area devoted to agriculture. A tributary of the East Fork Vermillion River flows south-southeastward through the lower western part of th…Lake County is a county in the U.S. state of South Dakota. As of the 2020 census, the population was 11,059. Its county seat is Madison. The county was formed in 1873. The terrain of Lake County consists of rolling hills, with the area devoted to agriculture. A tributary of the East Fork Vermillion River flows south-southeastward through the lower western part of the county, and Buffalo Creek flows southeastward from the central part of the county, leaving the county near its southeast corner. The terrain generally slopes to the south, although high points are found on the north and south boundary lines and points between.