The Goodman Theater’s 2006 production of “King Lear,” directed by Robert Falls and starring Stacy Keach, will be remounted next year by the Shakespeare Theater Company in Washington, D.C. Show will play in the theater’s recently opened Harman Center for the Arts, running June 16-July 19.The production launched Falls’ 20th anniversary season as artistic director of Chicago’s Goodman, becoming a much-discussed hit. Talk of potential transfers at the time was dampened due to other highly anticipated versions of the play, including a Public Theater production with Kevin Kline and the RSC’s staging with Ian McKellen, which toured to the U.S. Announcement of the D.C. run has sparked renewed speculation of a possible New York engagement to follow. In Falls’ version, Shakespeare’s tragedy is set in an Eastern European country akin to Yugoslavia at the time of its dissolution, depicting a morally bankrupt state collapsing into civil war. Keach will reprise his role as Lear in D.C., with much of the Chicago cast also expected to return.