Lamesa is a city in and the county seat of Dawson County, Texas, United States. The population was 9,422 at the 2010 census. Located south of Lubbock on the Llano Estacado, Lamesa was founded in 1903. Most of the economy is based on cattle ranching and cotton farming. The Preston E. Smith prison unit, named for the former governor of Texas, is located just outside of Lamesa.