Preheat the oven to 350°F (175°C).
Place the chicken breast-side down on a cutting board. Using kitchen shears, cut along both sides of the backbone and remove it. Flip the chicken over and press firmly on the breastbone to flatten it. Pat dry with paper towels.
In a small bowl, combine the softened butter, olive oil, Italian seasoning, paprika, black pepper, salt, and lemon zest.
Gently lift the skin of the chicken and spread some of the butter mixture underneath. Rub the remaining mixture over the top of the chicken.
In a large roasting pan, toss the carrots, potatoes, celery, and onion with olive oil, salt, and pepper.
Scatter the vegetables evenly and place the chicken on top. Squeeze fresh lemon juice over everything and drizzle a little extra olive oil over the chicken.
Roast for about 1 hour, or until the internal temperature of the thickest part of the chicken reaches 165°F (74°C). The skin should be golden and crispy.
Remove the chicken from the oven and let it rest for 10 minutes. Spoon pan juices over the chicken and vegetables before serving.