Lise Davidsen, one of opera’s biggest names, is preparing to leave the stage for a few months to give birth and spend time with twins. But she’s leaving fans with a gift: a recording of “The Flying Dutchman,” an opera she’s never performed and says she may never sing again. Davidsen says last year’s successful shows in Paris in “Salome” helped convince her to take on the role, as did the opportunity to record it in her native Norway and sing alongside baritone Gerald Finley, whom she long admired. The recording will be released April 18. Davidsen’s last performance before she goes on maternity leave will be Saturday in Beethoven’s “Fidelio” at the Metropolitan Opera.