Bring a deep pot of water to a boil. Plunge the lobster into the boiling water, head first, and cook for 3 minutes. Remove from the water and place in an ice bath to stop the cooking. Carefully halve the lobster lengthwise. Score the claws with a sharp knife, then the knuckle, to expose the meat. Discard the innards, if desired. Lay the lobster on a sheet pan, with the meat facing up and season it with the oil, and salt and freshly ground black pepper, to taste. Bake in the oven for 15 minutes or until the meat is cooked through.
Place the Crab and Shrimp Pasta in 2 bowls. Top with 1/2 a lobster and serve.
Crab and Shrimp Pasta:
Place a large pot of water for the pasta over high heat and bring to a boil. While the water is heating, in a small saucepan sweat the onions, Cajun seasoning, garlic, and shallots in oil over low heat. Add the tomatoes and cook for 15 to 20 minutes over a very low heat.
While the tomatoes are cooking, boil your pasta until al dente. Drain and set aside. Strain the tomato mixture through a fine-meshed sieve, making sure to get all the pulp possible, then transfer this to a saute pan. Over low heat, add the shrimp and crab. While stirring, add the butter in small pats until the sauce is a creamy texture. Add the oregano and basil, then check for seasoning. Do not let the sauce boil hard or it will break - keep it at a very low simmer. Add the pasta to the sauce and toss well.