Preheat oven to 400?F. Cook lobster according to package directions. Remove meat from shells and chop into 1-inch pieces.
Meanwhile, cook pasta according to package directions. Drain, reserving 1/3 cup cooking liquid. Grease 11- x 8-inch baking dish.
Melt butter in large skillet set over medium heat; cook onion, garlic and thyme for 3 to 5 minutes or until softened. Sprinkle flour over top; cook, stirring, for 2 to 3 minutes or until incorporated.
Slowly whisk in milk and cream; bring to boil, whisking constantly. Reduce heat to medium-low; cook, stirring constantly, for about 10 minutes or until thickened slightly. Stir in mustard, salt, pepper and nutmeg. Remove from heat.
Stir in 1 3/4 cups Gruyère and 1/4 cup Parmesan until melted. Stir in pasta, reserved cooking liquid and lobster. Transfer to prepared baking dish; sprinkle with remaining Gruyère and Parmesan.
Bake for 18 to 20 minutes or until golden and bubbly. Let stand for 10 minutes. Sprinkle with chives.