More than six years after a Broadway revival of 1964’s “Funny Girl” failed to get off the ground, Lauren Ambrose will get the chance to play the title role in another cherished musical: She will be Eliza Doolittle in the Lincoln Center Theater production of “My Fair Lady” opening this spring.

While names like Colin Firth were bandied about for the role of Henry Higgins, the part is going to an actor largely unknown in the United States: Harry Hadden-Paton, who has extensive theater experience in London, will be making his New York stage debut opposite Ms. Ambrose. On television Mr. Hadden-Paton played Bertie Pelham on PBS’s “Downton Abbey” and Martin Charteris on Netflix’s “The Crown.”

Lincoln Center Theater on Thursday announced key casting for the highly anticipated Broadway production, to be directed by Bartlett Sher, whose sumptuous revivals of “South Pacific” and “The King and I” enjoyed long runs and Tony Award recognition. Usually, the lead roles in “My Fair Lady” are not close to the same age, given its plot. In this case, Ms. Ambrose is 39 and Mr. Hadden-Paton is 36.

Also in the “My Fair Lady” cast: the two-time Tony Award winner Norbert Leo Butz, as Eliza’s jaunty father, Alfred P. Doolittle, and the Tony winner (and “Game of Thrones” alumnus) Diana Rigg as Henry Higgins’s mother.