Grate the zest from the lemon, lime, and orange into a large bowl. Squeeze the juice from half of each piece of fruit into the bowl. Whisk in 1 tablespoon barbeque sauce. Stir in ground beef; mix well. Cover and refrigerate for 10 to 30 minutes.
Preheat an outdoor grill for high heat, and lightly oil the grate.
Form meat into patties. Grill with lid open, about 3 minutes per side. Brush each burger with one tablespoon barbeque sauce during grilling, coating both sides. Top burgers with pepperjack cheese and cook until cheese is melted and meat is no longer pink in the center, about 1 additional minute.
