Lincoln Davis was a resident of Vault 3 in the 23rd century.
Lincoln Davis was one of the Vault's former Overseers, and endorsed Vault 3's final Overseer, George Stault, in his first or second campaign for Overseer. He was a well respected member of the community, and Stault felt that his endorsement won him the election. He presumably died or fled when Vault 3 was invaded by Fiends.
Lincoln Davis is mentioned only in Fallout: New Vegas.
Behind the Scenes
The name "Lincoln Davis" could be a reference to Abraham Lincoln, President of the United States, and Jefferson Davis, President of the Confederate States.