Heat the oven to 375°F and spread the rice evenly in a 9-by-13-inch baking dish.
Stir in the broth, onion, garlic, lemon zest, dill and 1 teaspoon salt.
Season the chicken cutlets with the remaining salt and black pepper and lay them over the rice.
Cover tightly with foil and bake until the rice is tender and the thickest cutlet reaches 165°F, 38 to 45 minutes.
Transfer the chicken to a plate and fold the spinach and lemon juice into the hot rice until the leaves wilt.
Return the chicken, scatter the feta over the dish and rest for 5 minutes before serving.