Heat oil in sauté pan. Add lobster (shell side down,) and clams. Cook until lobster shell begins to turn red and meat in tail section begins to firm up. Turn lobster over and add garlic. When garlic becomes translucent, add muscles, shrimp and tomatoes. Toss gently together with salt and cover.
Heat linguine in boiling water and drain well. Place in the center of a 15-inch platter. When clams and mussels open, sprinkle Italian parsley and toss gently. Place seafood attractively over pasta, making sure the shrimp are visible, and the lobster claw is cooked thoroughly and cracked open.