In a large, heavy-bottomed saucepan, melt 2 tbsp. butter in oil over medium heat. Add onion and cook until golden, about 5 minutes. Add carrots and celery and cook 5 more minutes. Add sausage and 1/2 tsp. salt, breaking up meat with a wooden spoon, and cook until meat loses its raw color.
Add 1 cup milk and cook over medium heat, stirring, until completely absorbed, 10 to 12 minutes. (The milk will appear quite curdled at this point; don't be alarmed.) Add wine and cook until reduced by half, about 3 minutes. Add tomatoes, bring to a boil, lower heat, and gently simmer, uncovered, 2 hours. Season with salt and pepper to taste.
After the ragù has cooked for 1 1/2 hours, make the béchamel by melting remaining 5 tbsp. butter in a heavy-bottomed saucepan over medium heat. Add flour and cook, stirring constantly, until it turns light golden brown, about 5 minutes. Slowly drizzle in remaining 3 cups milk, whisking constantly. Bring to a simmer and continue to cook, whisking, until thickened, about 10 minutes. Season with remaining 1 tsp. salt, nutmeg, and pepper to taste.
Preheat oven to 375°. Cook lasagna noodles according to package directions, being careful not to overcook. Drain and lay flat on dish towels, making sure the noodles do not overlap. Butter the bottom of a 9- by 13-in. baking dish and coat with about 1/2 cup of ragù. Add a single layer of noodles (for most brands this is 4 sheets per layer). Spread on 1/3 of the béchamel; top béchamel with 1/4 of the remaining ragù, then 1/4 of the parmesan. Repeat layering two more times, covering final layer with remaining ragù and parmesan.
Cover lasagna with buttered aluminum foil and bake 20 minutes. Uncover and bake an additional 10 minutes, or until the top browns slightly. Let sit 15 minutes before serving.
Note: Nutritional analysis is per serving.