Preheat the oven to 375 degrees Fahrenheit. In a small bowl, mix together the thyme, oregano, salt, and black pepper until combined. Set aside.
In a large bowl, toss together the potato, onion, and sliced lemon with 1/4 cup of the olive oil, 2 tablespoons of the lemon juice, and half the spice mixture until evenly coated. Empty the mixture into a 10 x 13-inch casserole dish.
In the same large bowl, toss the chicken with 1/4 cup of the olive oil, 2 tablespoons of the lemon juice, and remaining half the spice mixture until evenly coated. Nestle the chicken pieces into the pan, skin facing up (it's okay if there's potato/onion/lemon bits under them).
Cut the top 1/3 off the heads of garlic, and place them in the casserole dish, cut side facing up. Drizzle the top of each one with 1 teaspoon olive oil (making for 3 teaspoons total).
Pour the water into the pan, doing it in the pan's corner so it doesn't wash all the seasoning off the tops of the veggies and chicken. Place the pan in the oven and roast until the potatoes are tender when pierced with a fork, the chicken skin is golden, and the interior temperature of the chicken is at least 165 degrees Fahrenheit, about 1 hour to 1 hour and 20 minutes. Remove from the oven, top with the fresh dill, and enjoy immediately.