Adjust oven rack to middle position and heat oven to 375°.

Heat oil in large, heavy-bottomed Dutch oven over medium heat until shimmering but not smoking, about 2 minutes; add onion and cook, stirring occasionally, until softened but not browned, about 2 minutes. Add garlic and cook until fragrant, about 2 minutes. Increase heat to medium-high and add ground meats, salt, and pepper; cook, breaking meat into small pieces with wooden spoon, until meat loses its raw color but has not browned, about 4 minutes. Add cream and simmer, stirring occasionally, until liquid evaporates and only fat remains, about 4 minutes. Add pureed and drained diced tomatoes and bring to simmer; reduce heat to low and simmer slowly until flavors are blended, about 3 minutes; set sauce aside. (Sauce can be cooled, covered, and refrigerated for up to 2 days; reheat before assembing lasagna.

Mix ricotta, 1 cup Parmesan, basil, egg, salt, and pepper in medium bowl with fork until well-combined and creamy; set aside. Smear entire bottom of 9- by 13-inch baking dish with¼ cups meat sauce. Place 3 noodles on top of sauce. Drop 3 tablespoonfuls ricotta mixture down center of each noodle. Level by pressing flat with back of measuring spoon. Sprinkle evenly with 1 cup shredded mozzarella. Spoon 1½ cups meat sauce evenly over cheese. Repeat layering of noodles, ricotta, mozzarella, and sauce two more times. Place 3 remaining noodles on top of sauce, spread remaining sauce over noodles, sprinkle with remaining cups mozzarella, then with remaining¼ cups Parmesan. Lightly spray a large sheet of foil with nonstick cooking spray and cover lasagna. Bake 15 minutes, then remove foil. Return lasagna to oven and continue to bake until cheese is spotty brown and sauce is bubbling, about 25 minutes longer. Cool lasagna about 10 minutes; cut into pieces and serve.