Set a rack on the lower middle level of the oven and heat the oven to 425 degrees F.
Season the chicken inside and out with salt and pepper. Stuff the cavity with the thyme sprigs, garlic, and one lemon half, squeezing the lemon as you insert it to release the juice into the cavity. Rub the butter all over the chicken skin, including undersides, then season once again with salt and pepper.
Tie the ends of the drumsticks together with twine. Arrange the chicken breast-up on the rack in a roasting pan. Squeeze the juice of the remaining lemon half over the top of the chicken. (You can toss the lemon half into the roasting pan or discard it.)
Place the roasting pan in the oven. After 15 minutes, reduce the temperature to 350 degrees F. When the chicken is beginning to brown rapidly, baste with accumulated pan juices.
Add the onion, carrot, celery, and bay leaf to the roasting pan after 30 minutes. Continue roasting, basting several times, until the juices run clear when pierced at the thickest part of the thigh with a knife or if you tilt the chicken forward the juices that run out of the cavity are clear, an additional 45 to 60 minutes (1 1/4 to 1 1/2 hours total roasting time). Transfer the chicken to a cutting board, cover loosely with foil, and let rest in a warm place to allow the juices to redistribute, about 15 minutes. To serve, remove the herbs and the lemon half from the cavity and discard. Reserve the garlic cloves and carve the chicken. Serve the chicken with the vegetables and reserved garlic cloves. (The bay leaf may be left for decoration or discarded.)