Bring 6 quarts water to boil and add 2 tablespoons salt.
Crack lobster shells and remove meat. Cut tail into 1/2-inch slices and claws into 3 pieces. Set aside tomalley. In a blender, mix mint, basil, parsley, garlic, capers, tomatoes, black and red pepper and extra virgin olive oil to form smooth paste. If needed, add a little more olive oil. Pour pesto and lobster into large serving bowl.
Cook fettuccine according to package instructions until al dente and drain well. Pour hot pasta in bowl with lobster and toss like a salad until well mixed and serve immediately.