Preheat outdoor or indoor grill, OR oven broiler.
In a small saucepan, combine first 7 ingredients (tomato sauce through sugar); cook and stir over medium heat for 5 minutes.
In a small bowl or cup, combine olive oil and lemon juice; brush on fish. Grill/broil fish 4 inches from heat source for 5 minutes then turn and baste with tomato mixture; continue to grill/broil until fish flakes easily when tested with a fork. Allow 10 minutes total cooking time per inch of thickness, measured at its thickest part.
Thoroughly heat remaining tomato mixture and serve with fish.