Season chicken cavity with salt and pepper. Stuff chicken cavity with lemon chunks, celery, half of the thyme sprigs, half of the rosemary sprigs, and garlic cloves. Tie the legs together with kitchen string and tuck the wings underneath the bird. Place chicken in a large roasting pan.
Drizzle melted butter over the outside of the chicken. Season chicken liberally all over with salt and pepper.
Place potatoes, carrots and onion in a large Ziploc bag. Add olive oil to the bag, season with salt and pepper, and toss to coat.
Place the vegetables in the roasting pan around the chicken. Tuck the remaining sprigs of thyme and rosemary in the pan with the vegetables.
Roast the chicken and vegetables in the oven for about 1 1/2 hours, or until the meat reaches an internal temperature of 165 degrees F.