Preheat the oven to 350 degrees F (175 degrees C).
Make three slashes across each side of the fish using a sharp knife. This will keep the fish from curling as it cooks. Place the fish in a shallow baking dish or roasting pan. Cover each side with fresh ginger, then green onions and tomatoes. Season with sea salt. Slice half of the lime and place the slices on top of the fish. Drizzle with the soy sauce, and squeeze the other half of the lime over the fish. Cut the lemon in half and set in the pan. Cover the whole dish with aluminum foil.
Bake the fish until the flesh is opaque and can be flaked with a fork, about 20 minutes. Squeeze the baked lemon halves over the fish before serving. Serve the fillet on the top side first, then gently lift out the backbone, while helping the flesh off the bones with your knife. It's much easier than trying to turn the fish over.