Preheat the oven to 400 degrees F. Spray a 9x13-inch pan with nonstick spray.
Melt 5 tablespoons butter in a large pot over medium heat. Add the garlic and cook, stirring occasionally, for 1 minute. Whisk in the flour and cook 1 to 2 minutes until nutty and fragrant but not brown. Whisk in the cream and milk. Add the salt, bay leaf, and nutmeg and simmer 10 minutes.
Stir in 1/2 cup of the Romano cheese and 1/3 cup of the Swiss cheese, and cook an additional 5 minutes. Remove from the heat.
Melt the remaining 2 tablespoons of butter in a nonstick skillet over medium heat. Once melted, add the bread crumbs and stir occasionally until lightly golden, 1 to 2 minutes. Set aside.
To assemble the lasagna: Spoon 1/3 cup of the sauce over the bottom of the prepared baking dish. Use 4 lasagna noodles to cover the bottom of the dish. Spoon 2/3 cup sauce on top of the noodles, followed by half of the chicken and ham, 1/2 cup Swiss cheese and a sprinkle of the Romano. Repeat with another set of 4 noodles, 2/3 cup sauce, the rest of the chicken and ham, 1/2 cup Swiss and another sprinkle of Romano. Finish by layering 4 more noodles, the rest of the sauce and the remaining cheese, this time including the mozzarella.
Cover the pan with a sheet of foil that has been sprayed with nonstick spray, and bake 20 minutes. Remove the foil, top with buttered bread crumbs, and bake an additional 20 minutes, until the cheese is gooey and noodles are soft. Let rest 10 minutes before serving.