Fence Lake is a census-designated place located in southwestern Cibola County, New Mexico, United States. Designated in 1980 by the United States Census Bureau, Fence Lake had a population of 42 as of the 2010 census. The area is largely ranchland, and there are few businesses there. It was named after a small village which is contained within its bound…Fence Lake is a census-designated place located in southwestern Cibola County, New Mexico, United States. Designated in 1980 by the United States Census Bureau, Fence Lake had a population of 42 as of the 2010 census. The area is largely ranchland, and there are few businesses there. It was named after a small village which is contained within its boundaries.