Preheat oven to 350°F. 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. It's fine if you can't fit all of these ingredients into your chicken. Just stuff as much in there as you can! Tie the legs together with kitchen string and tuck the wings underneath the bird. Place chicken (breast-side up) in a large roasting pan.
Drizzle or brush melted butter over the outside of the chicken. Season liberally all over with salt and pepper.
Place potatoes, carrots, and onion in a bowl or large Ziploc bag. Add olive oil, 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 95-100 minutes, or until the meat reaches an internal temperature of 170°F when a thermometer is inserted into between a leg and thigh (not touching the bone). Let the chicken rest for 10-15 minutes before slicing and serving.