MIX dressing and half the lime juice. Pour over meat in shallow dish; turn to coat both sides of each steak. Refrigerate 30 min. to marinate.
MEANWHILE, mix remaining lime juice and barbecue sauce in medium bowl. Stir in all remaining ingredients.
HEAT grill to medium heat. Remove meat from marinade; discard marinade. Grill steak 17 to 21 min. or until medium doneness (160ºF), turning occasionally. Transfer to cutting board. Let stand 5 min. Cut steak across the grain into thin slices. Serve with bean salsa.