The path to change his status was cleared by a 2015 agreement (included as an exhibit in the suit) in which Mr. Levine extended his contract as music director through the summer of 2019. As music director he was paid $700,000 a year, plus $50,000 for travel and expenses, and $27,000 per performance — more than the $17,000 that the Met usually describes as its top fee. (Mr. Levine’s contract prohibited the Met from paying anyone more than him for performances, unless he agreed.)

The 2015 agreement, which came after years of health problems and cancellations, allowed the Met to make him music director emeritus should he be unable to perform his duties. During that season, 2015-16, Mr. Levine grew erratic at the podium, where the Met had previously built an elevator to accommodate his wheelchair. Musicians and singers said in interviews at the time that he had become hard to follow.

But when Mr. Gelb spoke to Mr. Levine about transitioning to emeritus status, he resisted.

“Astoundingly,” the lawsuit states, Mr. Gelb invited a reporter for The New York Times to attend a meeting with Mr. Levine and his neurologist, Dr. Stanley Fahn, that winter. The doctor said at the meeting that Mr. Levine’s most serious problems could probably be solved by adjusting the medication he was taking for his Parkinson’s disease.