In a deep saucepan, sauté the finely-chopped onion and carrot in a little oil and then add the chopped tomatoes and cook at a medium heat for about 15 minutes. Add the whole lobster, still alive, and cover, turn down the heat and cook for about 10 minutes. Take the lobster from the pan and cut it into pieces using poultry shears, put it back in the saucepan and cook for another 8 minutes. In the meantime, cook the spaghetti al dente in plenty of boiling salted water, drain and toss in a frying pan with the lobster sauce. Serve immediately piping hot. .