Cook the pasta according to directions, and drain.
Melt the butter in a large nonstick pot over medium heat and sauté the onion. Once the onion has been reduced, remove from heat and spread the flour in the pot. Slowly mix in the milk to get a smooth consistency. Place the pot back on the stove over medium-high heat, and mix regularly until the sauce is creamy.
Add the cheddar and Parmesan while continuing to mix so that they blend while melting.
Break the asparagus stalks from the bottom to remove the toughest part, then cut into chunks 2-3 cm in length. Place the asparagus and lobster meat in the sauce.
Finally, add the pasta, and garnish with mozzarella. Place the pot in the oven and grill at 350 °C for 20 minutes. Finish by broiling for 2 minutes.