Preheat the oven to 350 degrees F (175 degrees C).
Heat olive oil in a Dutch oven over medium-high heat. Season chicken thighs with lemon-pepper seasoning, 1 teaspoon salt, and 1/4 teaspoon garlic powder, rubbing the seasoning into both sides of the chicken. Cook chicken in the hot oil until browned, about 4 minutes per side. Transfer chicken to a plate and set aside.
Melt butter in the same pot and stir into the drippings. Add onion and cook, stirring occasionally, for 2 minutes. Turn off the burner.
Pour in chicken stock and water, scraping the bottom of the Dutch oven with a wooden or plastic spoon to loosen any browned bits. Stir in rice, lemon juice, remaining 1/2 teaspoon salt, remaining 1/4 teaspoon garlic powder, and pepper. Place the chicken on top of the rice and cover with the lid.
Bake in the preheated oven for 30 minutes. Uncover and remove the chicken to a plate using tongs. Stir rice from bottom to top then place the chicken back on top of the rice. Cook, uncovered, until all the liquid is absorbed and the rice is soft, about 15 minutes.