The authority’s vice chairman, Fernando Ferrer, will serve as acting chairman until Mr. Cuomo names a replacement. The State Senate, which will return to Albany in January, must confirm his pick.

Mr. Cuomo has called on state lawmakers to approve congestion pricing, a proposal to toll drivers entering the busiest parts of Manhattan, to pay for subway repairs. Mayor Bill de Blasio favors a tax on wealthy New Yorkers.

After Democrats won the State Senate this week, the party controls both legislative branches. They are expected to consider subway funding during the next session. The subway’s leader, Andy Byford, has proposed a sweeping overhaul plan that could cost $40 billion over 10 years. Congestion pricing is unlikely to cover the full cost of the plan and other sources might be needed.

Mr. Lhota served as an intermediary between Mr. Cuomo, a hard-charging leader who has taken a hands-on role at the agency, and Mr. Byford, who became president of New York City Transit in January after working at systems in Toronto and London. Mr. Lhota was also key in pressing Mr. Cuomo to support congestion pricing, even though it carried political risks, according to an official at the authority, who spoke on the condition of anonymity because he was not authorized to discuss the issue publicly.

Now Mr. Byford could be on his own, without someone to help him navigate the prickly task of working with Mr. Cuomo. Still, there are other leaders, including Veronique Hakim, the authority’s managing director, and Patrick J. Foye, its president. Ms. Hakim and Mr. Foye were interviewed for the M.T.A. chair job last year before Mr. Lhota’s return was announced. Ms. Hakim, the former head of New Jersey Transit, would have been the first woman to serve in the chair position.

Mr. Lhota did not respond to requests for comment about why he was leaving. In a statement, Mr. Lhota said that he had returned to the agency to halt the decline in service and argued that it had improved, pointing to a drop in train delays.