Preheat oven to 375°F. Cook pasta according to package directions until al dente; drain, transfer to a bowl, toss with oil and set aside.
Pull out about half of biggest, firmest pieces of lobster, and neatly slice into attractive pieces. Roughly chop remaining lobster.
Melt 4 tablespoons butter in 4-quart saucepan over medium heat. Add flour and cook, whisking constantly, until smooth, about 1 minute. Slowly whisk in milk and cook, continuing to whisk often, until sauce has thickened and coats whisk, about 10 minutes. Remove pan from heat and stir in mascarpone, along with clam juice, cayenne, and nutmeg; stir until smooth.
Return mixture to low heat and add 2 cups fontina, stirring until smooth; season with salt and white pepper. Add reserved pasta to cheese sauce. Stir in chopped lobster, half of chives, and half of scallions.
Transfer mixture to 9×13-inch or similar capacity baking dish and sprinkle with remaining fontina and cheddar cheese. In small bowl, melt remaining 2 tablespoons butter; combine with fresh bread crumbs, and sprinkle over top of pasta.
Bake 30 to 35 minutes, or until sauce is bubbly and pasta is browned on top. Let cool for 10 minutes. Garnish with remaining lobster slices, scallions, and chives.