Laurence Fishburne is going to Broadway next spring in a production of “Thurgood,” the one-man play by George Stevens Jr. about the former Supreme Court Justice Thurgood Marshall. The producer Bill Haber’s company, Ostar Productions, started making plans for Broadway after the show’s brief, sold-out run at the Westport Country Playhouse in 2006 with James Earl Jones in the title role. “Thurgood” will open on April 20 at the Booth Theater, with previews beginning on March 30.