Cook the rice according to the package directions.
Meanwhile, fill a pot with 2 inches of water, fit with a steamer basket, and bring to a boil.
Place the cabbage in the basket, cover the pot, and steam until tender, 15 to 20 minutes. Drain.
Meanwhile, heat broiler. Arrange the fish on a broilerproof baking dish and season with ½ teaspoon salt and ¼ teaspoon pepper.
Place 2 sprigs of dill, 3 lemon slices, and 1 tablespoon butter on top of each piece of fish.
Broil until the fish is opaque throughout, 10 to 12 minutes. Toss the rice with the zest and remaining butter. Serve with the fish and cabbage.