For the meat sauce: Process carrot, celery, and onion in food processor until finely chopped. Set aside. Process tomatoes and juice until finely chopped. Heat butter in heavy-bottomed Dutch oven over medium heat until foaming; add carrot, celery, and onion and cook until softened but not browned, about 4 minutes. Add ground meats and cook. Add milk and stir, breaking meat into ½-inch bits; bring to simmer and cook, stirring to break meat into small pieces, until almost all liquid has evaporated, 20 to 30 minutes. Using potato masher or wooden spoon, break up any remaining clumps of meat (no large pieces should remain). Add wine and bring to simmer; cook, stirring occasionally, until liquid has evaporated, 20 to 30 minutes. Stir in tomato paste until combined, about 1 minute; add chopped tomatoes, salt, and pepper. Bring to simmer, then reduce heat to medium-low and cook until sauce is slightly thickened, about 15 minutes. Transfer meat sauce to bowl and cool slightly. While meat sauce simmers, melt butter in medium saucepan over medium heat until foaming; add flour and cook, whisking constantly, until thoroughly combined, about 1½ minutes; mixture should not brown. Gradually whisk in milk; increase heat to medium-high and bring to full boil, whisking frequently. Add salt, reduce heat to medium-low, and simmer 10 minutes, stirring occasionally with heatproof rubber spatula or wooden spoon, making sure to scrape bottom and corners of saucepan. Transfer béchamel to bowl and cool slightly. Adjust oven rack to middle position; heat oven to 425 degrees. Place noodles in 13“ X 9” baking dish and cover with very hot tap water; soak 5 minutes, agitating noodles occasionally to prevent sticking. Remove noodles from water, place in single layer on kitchen towel, and pat dry. Wipe out baking dish and spray lightly with nonstick cooking spray. Stir béchamel to recombine; mix ¾ cup warm béchamel into warm meat sauce until thoroughly combined. Distribute 1 cup béchamel-enriched meat sauce in baking dish. Place three noodles in single layer on top of sauce, arranging them close together, but not touching, at center of pan. Spread 1¼ cups béchamel-enriched meat sauce evenly over noodles, spreading sauce to edge of noodles but not to edge of dish. Drizzle ⅓ cup béchamel evenly over meat sauce. Sprinkle ⅓ cup Parmesan evenly over béchamel. Repeat layering of noodles, béchamel-enriched meat sauce, bechamel, and cheese 3 more times. Place final 3 noodles on top and cover completely with remaining béchamel, spreading béchamel with rubber spatula and allowing it to spill over noodles. Sprinkle evenly with remaining Parmesan. Spray large sheet foil with nonstick cooking spray and cover lasagna; bake until bubbling, about 30 minutes. Remove foil, increase heat to 450 degrees, and continue to bake until surface is spotty brown, about 15 minutes. Cool 15 minutes; cut into pieces and serve.
