Lake is an unincorporated community in Logan County, West Virginia, United States. Lake is 4.5 miles east-northeast of Mitchell Heights. Lake has a post office with ZIP code 25121. The community was named after Nicholas Lake, the original owner of the town site. in 1863, after an executive order of Abraham Lincoln during the Civil War, he visited th…Lake is an unincorporated community in Logan County, West Virginia, United States. Lake is 4.5 miles east-northeast of Mitchell Heights. Lake has a post office with ZIP code 25121. The community was named after Nicholas Lake, the original owner of the town site. in 1863, after an executive order of Abraham Lincoln during the Civil War, he visited the town.