Cut chicken breasts in half (pound thin if necessary) and season with salt and pepper.
Add the flour, 4 eggs, and bread crumbs to 3 separate shallow dishes. Beat the eggs. Coat the chicken in the flour, then the eggs, and finally in the bread crumbs.
Heat the vegetable oil in a cast iron skillet over medium heat. Fry the chicken on both sides until golden brown, about 4 minutes on each side. Let drain on paper towels.
In a medium bowl, combine the ricotta cheese and the remaining egg.
Preheat the oven to 350°F (180°C).
Spread about ⅓ of the marinara sauce over the bottom of a casserole dish. Top with 4 lasagna noodles, ½ of the ricotta mixture, and 3 chicken cutlets. Sprinkle with ½ cup of mozzarella and ½ cup of Parmesan cheese. Repeat to make another layer, then finish with the remaining sauce and mozzarella and Parmesan cheeses.
Cover with foil and bake for 45-60 minutes, uncovering the lasagna for the last 10 minutes of baking.