Prepare the Ragù: Heat olive oil in a large pan. Sauté onion, carrots, celery, and garlic until soft. Add the ground meats, breaking them apart and cook until browned. Pour in the red wine, scraping the bottom of the pan. Add the crushed tomatoes and basil, season with salt and pepper, and simmer for about 30 minutes.
Make the Béchamel Sauce: In a saucepan, melt the butter, whisk in the flour until smooth, and cook for 2 minutes. Gradually add the milk, stirring constantly until the sauce thickens. Season with nutmeg, salt, and pepper.
Assemble the Lasagna: In a baking dish, layer béchamel sauce, lasagna noodles, ragù, Parmesan, and slices of mozzarella. Repeat the layers, finishing with béchamel and a generous sprinkle of Parmesan.
Bake: Cover with foil and bake in a preheated oven at 375°F (190°C) for 45 minutes. Remove the foil and bake for an additional 15 minutes until golden and bubbly.