In a large bowl, mix the tomato sauce, barbeque sauce, Worcestershire sauce, vinegar, mustard, and brown sugar. Place the lamb chops into the mixture, and marinate in the refrigerator at least 20 minutes.

Preheat an outdoor grill for high heat.

Cook the lamb chops about 10 minutes on the prepared grill, turning frequently and basting often with the marinade. The internal temperature of the chops should reach a minimum of 145 degrees F (63 degrees C).