NGS Style Manual‎ > ‎- G -‎ > ‎

governor, lieutenant governor

Never abbreviate governor.

Capitalize before personal name but not when formal title is in apposition:
            Governor Sloan
            Christopher P. Sloan, governor of Colorado
            Christopher P. Sloan, Colorado's governor
            Christopher P. Sloan, governor of the state
            the governor of Colorado
            the governor

            Lt. Governor John L. Eliot
            Lt. Governor Eliot
            the lieutenant governor