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 chili pepper and extra-virgin olive oil to form smooth paste. If needed, add a little more olive oil. Pour pesto into large serving bowl.
Cook fettuccine according to package instructions until al dente. Add lobster into the pasta cooking water for 1 minute. Drain well. Pour hot pasta and lobster into the bowl and toss like a salad until well mixed and serve immediately. Sprinkle with chopped parsley leaves.
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