Preheat the oven to 425 degrees F.
Prepare the chicken by removing any giblet packets from inside.
Use paper towels to pat the chicken dry inside and out. Be thorough about drying the chicken as it will help produce a crispier skin.
Sprinkle 2 tsp of coarse salt on each side of the chicken. Rub the salt into the skin before flipping it over (I start on the breast side) and adding salt to the other side.
Peel the skin off one onion and quarter it. You can half it if it is on the smaller side.
Quarter a lemon.
Stuff the inside of the chicken with the lemon wedges, quartered onion, and sprigs of sage, rosemary, and thyme. Set aside.
Prepare the vegetables. Wash and peel the carrots. Cut off the top and a small piece at the bottom and discard. Cut the carrots into approximately 2-inch pieces, then cut the pieces in half vertically down the middle. If the carrots are on the skinnier side, leave them in the 2-inch chunks.
Wash the potatoes and cut any that are particularly large in half. The goal is to have the potatoes roughly the same size so that they cook evenly.
Remove the skin from the remaining 2 onions and quarter them.
Place the prepared carrots, potatoes, and onions in the bottom of the Dutch oven.
Drizzle olive oil (about 2 tbsp) over the vegetables.
Sprinkle the vegetables with 1 tsp Herbes de Provence. Lightly salt and pepper. Toss everything with your hands to combine.
Place the prepared chicken on top of the vegetables. Drizzle with 6-7 tbsp of olive oil and rub the oil over the surface of the chicken. Be sure to get the oil into the crevices like the inside of the thighs and wings.
Cover the pot and cook at 425 degrees for 1 hour and 15 minutes for 5 lbs to 1 hour and 30 minutes for 6 lbs.
Remove the cover and finish roasting for approximately 20 minutes. If you notice the pan is dry (it usually makes its own pan juices), you can add a touch of low sodium chicken broth so the vegetables won't burn.
The chicken is done when an instant-read thermometer placed into the thickest part of the chicken thigh and chicken breast registers 165 degrees F.