Four consecutive performances of Lincoln Center Theater’s acclaimed “Carousel” revival were canceled last week when Michael Hayden, who stars as Billy Bigelow, bruised a vocal cord and understudy Duane Boutte was downed with a bronchial infection. The shows affected were Wednesday matinee through Friday evening.Producers tapped Marcus Lovett, Broadway’s current “Phantom of the Opera,” to take over the role. Lovett began rehearsing with director Nicholas Hytner Thursday and was expected to perform the role of Billy beginning with the Saturday matinee. Producers estimate that the four lost performances have cost them at least $ 100,000, with most ticket holders asking for exchanges rather than refunds, according to a spokesman for the show. “Phantom” producer Cameron Mackintosh, who also licensed the Lincoln Center production, released Lovett from his contract a week early to join “Carousel.” Hytner jetted in from England last week to rehearse Lovett. Hayden could be back at work by Tuesday, following a doctor’s appointment, although such injuries can be stubborn. A “Carousel” spokesman said that once the various ailments have subsided, Hayden would return to the lead, Boutte would continue as understudy and Lovett would remain on standby.