Fish: Put an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Spray a small baking sheet or glass baking dish with vegetable oil cooking spray. Set aside.
In a small bowl, whisk together the lemon juice, 3 tablespoons of olive oil, garlic, salt, and pepper until smooth. Pour the mixture into a sealable plastic bag or a glass baking dish. Add the halibut and coat it with the lemon mixture. Refrigerate for 35 minutes. Remove the halibut from the marinade and arrange them on the prepared baking sheet. Roast until the fish flakes easily with a fork, about 15 to 18 minutes.
Salad: Heat the oil in a medium skillet over medium-high heat. Add the shallots and red bell pepper. Season with salt and pepper, to taste. Cook, stirring frequently, until the shallots are soft and translucent, about 6 minutes. Turn off the heat, then add the peas, the chopped mint, lemon zest, and thyme. Drizzle with the remaining 2 tablespoons of olive oil and toss to coat. Season with salt and pepper, to taste.
Spoon the salad onto 4 plates and top with the halibut. Garnish with mint sprigs and serve.