Choreographer Wayne McGregor will take over supervision of the production, which opens on November 19.
General director William Mason said that Hall's concept for the staging would remain intact. "The direction and groundwork have been firmly set for this wonderful production," he said. "This is a Peter Hall production."
McGregor, the founder of London's Random Dance, has been working closely with Hall on the production, which uses dance extensively.
"Peter Hall, [music director] Andrew Davis, and I have every confidence in Wayne's ability to ensure the success of The Midsummer Marriage," Mason said. "We have all been greatly impressed with Wayne's brilliant choreography for this work."
According to a statement from the Lyric, Hall told the cast on November 3 that he had been ill for several days and that his doctor had advised him to stop working. "I feel great disappointment at not being able to finish this, but I couldn't leave it in better hands," Hall said. "The show is well advanced, with lots of juice and excitement in the cast. "
Hall is the founder of the Royal Shakespeare Company and the former director of the Royal National Theatre; his Broadway credits include Amadeus and Betrayal. The former artistic director of Glyndebourne Festival Opera, he has directed operas at Covent Garden, the Metropolitan Opera, Bayreuth, and elsewhere. He has created four productions for the Lyric since 1993.