First Citizen

First Citizen is the title held by the governors of Vault City, after they've left the Vault 8 and abandoned the title of Overseers. It is unclear what their prerogatives are, but they are head of the state, deal with Vault City's foreign policies, and revoke citizenships with gusto.

At the time of Fallout 2, Lynette is the First Citizen of Vault City.

Behind the Scenes
This is possibly a reference to Issac Asimov's "Foundation Trilogy" in which the character known as "The Mule" makes himself the first citizen of the planet Klagan which he captured earlier