“Abraham Lincoln’s Big, Gay Dance Party,” which played a buzz-attracting run in the 2009 New York Intl. Fringe Fest, will hit Off Broadway this summer for a six-week run.Play by Aaron Loeb centers on a fourth-grade Christmas pageant in Illinois that sparks controversy by questioning Lincoln’s sexuality. Chris Smith, who also helmed the show at the Fringe, directs. “Dance Party” originated at the SF Playhouse in 2008. Off Broadway incarnation, produced by BlueRare Prods., begins previews July 27 for an Aug. 12 opening at the Acorn Theater at Theater Row.