Preheat the oven to 400 degrees F (200 degrees C).

Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in the boiling water, stirring occasionally until tender yet firm to the bite, about 8 minutes. Drain.

Melt butter in a saucepan over medium heat; stir in cream cheese until it begins to melt, about 5 minutes. Season with salt, onion powder, and black pepper. Gradually whisk warm milk into cream cheese until smooth; stir in 1 1/2 cups Swiss cheese. Bring sauce to a simmer, stirring constantly, until cheese has melted and sauce has thickened, 5 to 10 minutes. Remove from heat.

Spread 3/4 cup cheese sauce into the bottom of a 9x9-inch baking dish. Arrange 1/3 lasagna noodles over sauce; spread 1/2 cooked chicken and 1/2 ham over noodles. Pour 1 cup sauce over top. Repeat layers starting with 1/2 remaining lasagna noodles, remaining 1/2 chicken, remaining 1/2 ham, and 1 cup cheese sauce. Layer on remaining lasagna noodles, remaining sauce, remaining 1/2 cup Swiss cheese, and bread crumbs; sprinkle top with Italian seasoning. Cover dish with aluminum foil.

Bake in the preheated oven until bubbling, about 25 minutes. Remove foil; continue baking until bread crumbs are browned, about 10 minutes more. Let casserole stand before serving, 5 to 10 minutes.