Dawson County is a county located in the U.S. state of Nebraska. As of the 2010 census, the population was 24,326. Its county seat is Lexington.Dawson County is part of the Lexington, NE Micropolitan Statistical Area.In the Nebraska license plate system, Dawson County is represented by the prefix 18 (it had the eighteenth-largest number of vehicles registered in the county when the license plate system was established in 1922).