Lexington - Subject to local approval, clarifies that vacancies on the board of mayor and aldermen and in the office of mayor be filled by majority vote of the remaining board members, with the appointee to serve only until the next regular election, at which time the remaining unexpired term is filled; authorizes mayor to vote in board matters but only to break a tie vote; removes city residency requirement for certain officers and managers by allowing such persons to reside in the county. - Amends Chapter 402 of the Acts of 1901; as amended and rewritten.