Preheat oven to 400°F (200°C). Lightly grease a 9x9-inch baking dish and set aside.
Boil salted water in a large pot. Cook lasagna noodles until al dente, about 8 minutes, stirring occasionally. Drain and set aside.
Melt butter in a saucepan over medium heat. Add cream cheese and stir until mostly melted, about 5 minutes.
Season with salt, onion powder, and pepper. Gradually whisk in warm milk until smooth. Stir in 1½ cups Swiss cheese until melted and thick. Remove from heat.
Spread ¾ cup sauce in the baking dish. Add a third of the noodles, half the chicken and ham, then pour 1 cup of sauce over.
Add half the remaining noodles, the rest of the chicken and ham, and another cup of sauce. Top with final noodles and remaining sauce.
Sprinkle ½ cup Swiss cheese, then breadcrumbs. Finish with a pinch of Italian seasoning.
Cover with foil and bake for 25 minutes. Uncover and bake 10 more minutes until golden and bubbly.
Let sit for 5–10 minutes before slicing to keep layers intact.