Heat 1 tablespoon of oil in a large saucepan. Add the carrot, onion, and garlic and saute until the onion is translucent, about 5 minutes. Stir in the lentils. Add 2 1/2 cups of broth and bring to a boil over high heat. Decrease the heat to medium-low. Cover and simmer gently until the lentils are just tender, about 15 minutes. Drain well. Transfer the lentils to a large bowl.

Meanwhile, bring the remaining 2 cups broth and bay leaf to a boil in a medium saucepan over high heat. Add the rice and return the broth to a simmer. Cover and simmer gently over low heat until the rice is tender and the liquid is absorbed, about 20 minutes (do not stir the rice as it cooks). Remove the saucepan from the heat. Fluff the rice with a large fork. Transfer to the bowl with the lentils. Add the olives, parsley, thyme, and lemon peel. Toss the rice mixture with the remaining 3 tablespoons oil to coat. Season, to taste, with salt and pepper. Serve warm or at room temperature.