John was the son of John and Elizabeth Camp. After graduating from the University of Tennessee in 1848 he moved to Gilmer in Upshur County, Texas. He started a plantation and was admitted to the bar. In 1851 he married Mary Ann Ward, the daughter of a local doctor. The couple had five children, including John Lafayette, Jr.
Camp joined the 14th Texas Cavalry for service to the Confederacy at the outbreak of Civil War, and was elected Captain of his company. By the end of the war, he was Colonel of the 10th Texas Cavalry, and attached to the Army of Tennessee. He saw action at Cumberland Gap, Murfreesboro, and Chickamauga. Camp was wounded and captured twice.
In 1866, the first district in Texas elected Camp to the U.S. Congress. However, in the struggle over seating of delegations connected with the Reconstruction, he was not allowed to take his seat. He remained active in Democratic Party politics.
Camp was elected to the Texas State Senate in 1874, and served from 1875 to 1878, when Governor Richard Hubbard appointed him a judge in State district court. He resigned from the bench in 1878 due to poor health.
Camp moved to Arizona in 1884 and worked as a registrar in the land office. When the drier climate failed to improve his health, he came back to Texas two years later. He settled in San Antonio, living in his later years with his son, John, Jr. He died there in 1891 and is buried in the Dignowitty Cemetery.
Camp County, Texas was named for him after he introduced the Bill in the state Senate that created the county.