Preheat your oven to 375°F (190°C) and lightly grease a 9x13 inch casserole dish with avocado oil. Set aside.
In a large pot, bring about an inch of water to a boil. Add a steamer basket, then place the broccoli florets inside. Cover and steam for 3-4 minutes until bright green and tender-crisp. Remove from heat, then transfer broccoli into a bowl and set aside.
In the same pot, heat the remaining avocado oil over medium heat. Add the chopped onion, garlic, and diced carrots. Sauté for 6-8 minutes until softened and fragrant, then remove from heat.
In a large mixing bowl, combine shredded chicken, steamed broccoli, sautéed onion and carrot mixture, yogurt, sour cream, 1 cup of shredded cheddar, dried dill, dried onion seasoning, salt, thyme, garlic powder, lemon juice, lemon zest, and optional cooked brown rice. Stir everything together until well combined.
Transfer the chicken and vegetable mixture into the greased casserole dish, spreading it out evenly. Top with the remaining 1/2 cup of shredded cheddar cheese.
Bake the casserole in the preheated oven for 35-40 minutes or until the cheese is bubbly and lightly golden. Allow it to cool for about 10 minutes before serving.