Preheat the oven to 500 degrees F. Rinse the chicken and pat dry. Season with salt and pepper, then place skin-side up on a rimmed baking sheet. Squeeze 1/2 lemon over the chicken and drizzle with 1 tablespoon olive oil. Roast 15 minutes. Meanwhile, cut the potatoes and radishes in half and cut the scallions into thirds. Toss the potatoes, radishes, carrots and the remaining 2 tablespoons olive oil in a bowl; season with salt and pepper. Remove the chicken from the oven and scatter the vegetables around it. Continue to roast until the vegetables are tender and the chicken is golden and cooked through, about 20 more minutes. Squeeze the remaining 1/2 lemon over the chicken and vegetables. Top with the dill and season with salt.