Set the oven temperature to 400°F (200°C).
Fill a big pot with water, add a little salt, and bring it to a boil. Add lasagna and cook until al dente, stirring occasionally, for about 8 minutes. Drain and set aside.
On medium heat, melt butter in a saucepan. Add cream cheese and mix until partially melted, taking about 5 minutes. Season with salt, onion powder, and pepper. Gradually whisk in warm milk until the mixture is smooth. Add 1 1/2 cups of Swiss cheese and stir until melted and thickened, then remove from heat.
Put 3/4 cup of cheese sauce at the bottom of a 9×9-inch baking dish. Layer a third of the lasagna noodles over the sauce, then add half of the chicken and ham. Pour 1 cup of sauce over the topping.
Layer with half of the leftover noodles, chicken, ham, and 1 cup cheese sauce. Top with remaining noodles, sauce, 1/2 cup Swiss cheese, and bread crumbs. Sprinkle with Italian seasoning. Cover the dish with foil.
Bake in the oven for about 25 minutes until the dish is bubbling. Uncover and bake until the crumbs are golden brown, about 10 more minutes. Let it stand for 5 to 10 minutes before serving.