Place flour on a plate. Beat eggs in shallow bowl; place 1 cup cheese on another plate.
Working with 1 cutlet at a time, coat the chicken with the flour, then egg, then cheese, pressing to adhere. Transfer to a plate.
Bring a large pot of water to a boil. Add salt, then the pasta and cook until al dente, 3 minutes. Drain, reserving a ladleful of water.
In a large nonstick skillet, heat 2 tbsp EVOO, over medium heat. Add chicken and cook, turning once, until golden, 10 minutes. Transfer to a platter and keep warm. Add 1 tbsp EVOO, to the skillet. Add sliced lemon, garlic and capers and cook for 2 minutes. Stir in the wine and parsley and cook until reduced, 1 minute. Lower the heat and bring to a simmer.
Stir the chicken broth into the sauce for 1 minute. Stir in the butter until melted, then stir in the lemon juice. Spoon a little sauce over the chicken. Add the spinach to the remaining sauce in the skillet and cook until wilted. Add the reserved pasta cooking water. Stir in pasta and toss to coat; season with salt and pepper. Add the remaining 1/4 cup cheese and toss. Serve the pasta with the chicken.