Lamesa is the seat of Dawson County, Texas, United States. Located south of Lubbock on the Llano Estacado, Lamesa was founded in 1903. Most of the economy is based on cattle and cotton. A prison is being constructed in Lamesa. Lamesa apartments for rent comparison page shows most up to date rent information on Lamesa apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.