While the veggies are cooking, place a medium-size sauté pan over medium-high heat and melt the butter. Whisk in the flour and cook the mixture for about 1 minute. Whisk the milk into roux, breaking up any clumps. Bring the mixture to a bubble and add the pumpkin puree and nutmeg. Season the sauce with salt and freshly ground black pepper, reduce the heat and simmer the sauce for 2-3 minutes, until slightly thickened.
Spread about 1 cup of the sauce into the bottom of a 13 x 9" casserole dish. Layer three lasagna noodles over the sauce, then top them with about 1 cup of the meat mixture, a cup or so of the sauce and a palmful of cheese. Repeat these layers two times, topping the casserole with a layer of lasagna noodles. Spoon the remaining sauce over the noodles, sprinkle the remaining grated cheese over top. Cover with aluminum foil and bake the lasagna until the sauce is bubbling and pasta is baked through, about 45 minutes.
During the last ten minutes of baking, remove the aluminum foil to brown the cheese. Once out of the oven, allow the dish to rest a few minutes before serving.