Joseph J. Lhota, the New York Metropolitan Transportation Authority chairman, resigned Friday after Gov. Andrew Cuomo was reelected to a third term, according to a state official. Lhota, who was hired to help turn around the city’s crumbling subway system, has been under fire for potential conflicts of interest that were brought to light in an investigation by The New York Times earlier this year. While serving as chairman, Lhota kept his job at N.Y.U Langone Health, and joined the board of Madison Square Garden, which is actively involved in negotiations with the MTA about the future of Penn Station. Lhota had previously held the position of MTA chairman, helping the crisis-ridden system rebound after Hurricane Sandy. Lhota told reporters earlier this year that he would remain in the position until 2021.