Arrange tomatoes, cut side up, in a 9- by 13-inch baking pan. In a small bowl, mix onions, garlic, chopped dill, oil, and water. Distribute onion mixture over tomatoes. Bake on top rack of a 425-degree F oven for 25 minutes.
Rinse fish and pat dry; then cut into 4 equal pieces, if necessary. Place fish in a baking pan large enough to hold pieces in a single layer. Drizzle with lemon juice, cover, and place in oven, setting pan on bottom oven rack.
Continue to bake fish and tomatoes until tomatoes are lightly browned on top and fish is just opaque but still moist in thickest part; cut to test (8 to 10 minutes).
Transfer fish to a platter. Add fish cooking juices to tomato mixture and stir well; spoon over fish. Garnish with dill sprigs, if desired.