Preheat oven to 375°. In a large pot of salted boiling water, cook cavatappi until al dente, about 1 minute or 2 less than the package instructions, it will finish cooking in the oven. Drain the pasta and set aside.
First you're going to make a roux. In a large saucepan over medium heat, melt butter. Sprinkle over flour and cook until slightly golden, 2-3 minutes. Stir it often to ensure it doesn't burn or stick to the pan. Pour in milk and whisk until combined. Season with salt, and pepper. Let simmer until thickened, about 2 minutes.
Remove pan from heat and stir in cheddar, Fontina, mozzarella, and 1/2 cup Parmesan (reserve remaining 1/4 cup) and whisk until smooth. Gently fold in pasta and lobster meat and transfer into a 9"-x-13" baking dish.
In a medium bowl, combine Panko, the remaining Parmesan, and oil. Season with salt and pepper and sprinkle over pasta.