Preheat the oven to 425 degrees F. Place the halibut in a parchment paper-lined baking dish. Drizzle with lemon juice and 1 Tbsp. of the oil; season with salt and pepper.
Place remaining oil in a skillet set over medium heat. Add mushrooms, onion, green pepper and carrots and sauté 4 minutes. While the vegetables cook, bake the halibut for 12 to 15 minutes, or until cooked through.
When the vegetables have cooked 4 minutes, add the wine, tomato sauce and sugar. Bring to a simmer, and simmer 5 minutes. Stir in the pesto; season with salt and pepper.
When the fish is cooked, plate, top with sauce, and serve.