Bring a large pot of lightly salted water to a boil. Cook cavatappi in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain. Preheat oven to 375 degrees F (190 degrees C). Melt butter in a saucepan over medium-low heat. Stir in flour until a paste forms, about 2 minutes. Stir in heavy cream slowly; cook until heated through, 3 to 5 minutes. Add 1 package Swiss cheese and 1 package Cheddar cheese; stir until melted, about 2 minutes. Season sauce with nutmeg, salt, and pepper. Combine cooked pasta, sauce, lobster, and lobster cooking liquid in a large bowl. Stir in half of the remaining Swiss cheese and Cheddar cheese. Transfer to a 9x13-inch baking dish. Sprinkle remaining Swiss cheese and Cheddar cheese on top. Bake in the preheated oven until cheeses are melted and bubbly, 20 to 30 minutes.