Stir ricotta cheese, 1/2 of the mozzarella cheese, 1/2 of the Parmesan cheese, and Italian seasoning together in a bowl.
Lay pounded chicken breasts on a work surface; spoon 2 tablespoons cheese mixture into the center of each chicken breast. Roll chicken around cheese and secure with a toothpick. Repeat with remaining chicken breasts. Place rolled chicken into a 9x13-inch glass baking dish. Spread mushrooms around chicken and pour white wine and lemon juice over the top. Scatter 1/2 of the butter over chicken and sprinkle remaining mozzarella cheese and Parmesan cheese over the top.
Bake in the preheated oven until chicken is no longer pink in the middle and juices run clear, 40 to 45 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain, return penne to the pot, and stir remaining butter into pasta. Ladle pasta into bowls, place chicken over pasta, and spoon pan juices over the top.