Toss the asparagus with a small amount of olive oil and roast in a 400°F oven for 15 minutes.
Make the white sauce with the next six ingredients. Mix the eggs and ricotta cheese together and add this to the white sauce.
Cook the lasagna noodles as directed on the package.
Coat the noodles with sauce and lay them in a 9x13-inch casserole dish that has been coated with oil or nonstick spray. Distribute half of the chicken and asparagus over the noodles and sprinkle with Parmesan cheese. Add another layer of noodles, followed by the rest of the chicken and asparagus and another sprinkle of Parmesan. Add a final layer of noodles topped with white sauce and mozzarella cheese.
Bake the lasagna at 400°F for 30 minutes.
While the lasagna is baking, prepare the marinara sauce: In a quart saucepan, sauté the onions and carrots in butter. Stir in the tomatoes, basil, salt, pepper, and sugar. Cover and simmer for 15 minutes. Puree in blender until smooth. Return to the saucepan, add the chicken stock, and reheat.
When the lasagna has finished baking, remove it from the oven and let it sit for 15 minutes. Serve topped with marinara sauce and sprinkled with Parmesan cheese.