Houghton Mifflin Harcourt announced on Sunday that it had acquired the United States rights to publish a previously unknown work by J. R. R. Tolkien, “The Fall of Arthur.” The book, set for publication in May, chronicles the last days of King Arthur and will be edited by Tolkien’s son Christopher, who will also provide commentary and notes. Tolkien, the author of “The Lord of the Rings,” died in 1973. This is the first new work by him to be unearthed since “The Legend of Sigurd and Gudrun” was released in 2009.