Lamb County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 13,977. Its county seat is Littlefield. The county was created in 1876 but not organized until 1908. It is named for George A. Lamb, who died in the Battle of San Jacinto.Lamb County was the home of the Texas House Speaker Bill W. Clayton, who served from 1975 until 1983.The historic Triple Arrow Ranch in Lamb County is owned by Commissioner's Court Judge William A.