LONDON — New productions of James Baldwin’s “The Amen Corner,” helmed by Rufus Norris, and “King Lear,” helmed by Sam Mendes, headline the packed National Theater 2013-2014 slate announced Wednesday by a.d. Nicholas Hytner.Baldwin’s classic Harlem-set play about faith, music and family, starring Marianne Jean-Baptiste and Sharon D. Clark will play the Olivier, the three-theater venue’s largest stage. Opening in June, Norris’ production follows Hytner’s own previously announced production of “Othello,” starring Adrian Lester, Rory Kinnear and Lyndsey Marshal. Further productions on the Olivier stage will include Christopher Marlowe’s “Edward II,” starring John Heffernan, helmed by Joe-Hill Gibbins in his NT debut. For the NT’s family show slot at Christmas, Carl Miller will adapt Erich Kastner’s 1930s classic adventure story “Emil and the Detectives” in a production by Bijan Sheibani. Mendes’ production of “King Lear,” starring Simon Russell Beale, will preem in January 2014. Unseen in London since 1985, Eugene O’Neill’s epic “Strange Interlude” will be given a rare staging in the NT’s Lyttelton theater. Starring Anne-Marie Duff and Charles Edwards, the production is helmed by Simon Godwin in his NT debut. Later in the year, former a.d. Richard Eyre returns to direct Pirandello’s “Liola” in a new version by Tanya Ronder. Tori Amos and Sam Adamson’s much delayed tuner adaptation of George MacDonald’s “The Light Princess” will play the Lyttelton in October. Helmed and lit by the “War Horse” team of Marianne Elliott and Paule Constable, the show has a cast headed by rising star Rosalie Craig (“Finding Neverland”) and Clive Rowe. With the Cottesloe, the NT’s most versatile auditorium, about to close as part of the org’s £70 million ($111 million) building program, Hytner announced the February opening of a one-year temporary theater, The Shed. A highly versatile 225-seat steel and timber building, it has cost $2.8 million, funded entirely by the profits from the Gotham production of “War Horse.” It will host a raft of new commissions plus presentations from small-scale regional venues. In January 2014, it will preem a new play examining gender by Nick Payne (“If There Is I Haven’t Found It Yet,” “Constellations”) and helmed by Carrie Cracknell (“A Doll’s House”). Speaking at the launch of this, the 50th anniversary season, Hytner pointed to record stats for the U.K.’s flagship theater org. Thanks to multiple touring dates at home and abroad, plus NTLive cinema screenings in 23 countries, in 2012 the NT had a worldwide audience reach of 3.2 million, its productions accounting for 35% of total playgoing in London. This spring, the NT will hit a record level of output with four West End transfers running concurrently with its home and international productions. To celebrate the October anniversary, the BBC will screen a series of documentaries devoted to the building, its history and workings.