Melt butter in a medium saucepan over medium. Stir in flour and salt, and cook, stirring often, until mixture begins to turn a light blond color, about 2 minutes. Whisk in Marsala until absorbed. Gradually whisk in milk until combined. Reduce heat to medium-low; cook, stirring occasionally, until mixture thickens and coats the back of a spoon, about 10 minutes. Stir in mushrooms; remove from heat. Add fontina, nutmeg, and pepper, and stir until cheese is melted. Set béchamel aside.

Stir together turkey, gravy, Parmesan, and sage in a large bowl until combined. Refrigerate until ready to use.

Melt butter in a small saucepan over medium. Cook, stirring occasionally, until butter begins to brown, about 3 minutes. Remove from heat, and stir in squash, Parmesan, and nutmeg. Transfer squash mixture to a food processor; process until smooth, about 2 minutes. Set filling aside.

Preheat oven to 350°F. Grease a 13- x 9-inch baking dish with cooking spray. Bring a large pot of salted water to a boil over high. Add lasagna noodles, and cook, stirring often, 6 minutes. Remove noodles from water, and let drain.

Spoon half of the mushroom béchamel in an even layer on bottom of prepared dish. Top with a layer of cooked noodles; spread half of the turkey filling over noodles. Repeat noodle layer; top with all of the butternut squash filling. Repeat noodle layer; top with remaining turkey filling. Repeat noodle layer; top with remaining mushroom béchamel. Sprinkle with fontina. Spray a sheet of aluminum foil with cooking spray (to prevent sticking), and cover lasagna with foil; place on a large rimmed baking sheet.

Bake in preheated oven 1 hour. Remove foil, and bake until bubbly and browned, about 15 minutes. Let stand 30 minutes. Just before serving, heat butter in a medium skillet over medium-high. Add sage leaves, and cook until crisp, 30 seconds to 1 minute. Sprinkle over lasagna.