Place oven rack in lowest position and preheat oven to 250 degrees F.
Place 6 quart, oven-proof, Dutch oven on stove. Add olive oil.
Remove giblets from chicken and discard. Tuck wings under back. Pat chicken dry using paper towels. Season with salt and pepper.
Over medium heat, heat the oil in the Dutch oven. Place chicken in pot, breast-side down. Distribute remaining ingredients, except the lemon juice, around the chicken. After about 5 minutes, when chicken is light brown, turn chicken breast-side up. Cook 6 - 8 minutes, until chicken and vegetables are well browned. Remove from heat.
Cover the pot tightly with foil. Place the lid on top to seal tightly. Place in oven. Cook until instant-read thermometer reaches 160 degrees F in the thickest part of the breast and 175 degrees in the thickest part of the thigh, about 80 to 110 minutes for a 3 1/2 - 4 1/2 pound chicken and closer to 2 hours for a 5 - 6 pound chicken.
Place chicken on carving board, tent with foil, allow to rest 20 minutes. Place a serving platter in the oven to warm.
Meanwhile, using fine-mesh strainer, pour juices from pot into fat separator. Press on solids to extract liquid; discard solids. There should be about 3/4 cup juices. Allow fat to separate, about 5 minutes. Place a small saucepan over low heat, pour in juices, without the fat, and stir in lemon juice.
Carve chicken and place on warm platter. Add any additional juices to saucepan, adjust with additional lemon juice or salt and pepper, if necessary. Serve chicken, passing the jus.
Freeze or refrigerate chicken carcass to make stock or soup.