If cooking a live lobster, bring a large pan of salted water to the boil. (If using a ready-cooked fresh lobster, proceed to the next step.) When the water is boiling, place the lobster into the water head first and bring back to the boil. Cook for 10-12 minutes. The lobster will change colour from green-brown to bright red as it cooks. Remove the lobster from the water and allow to cool.
Remove the meat from the lobster, reserving the shells. First remove the large claws by twisting and pulling the front legs where they connect to the body. Then break the leg away from the claw.
Use a sharp knife to split the claw shell, then remove the claw meat. Repeat with the other claw.
Using the handle of a fork or spoon and a sharp knife, remove the nugget of meat from the legs.
To remove the meat from the body, stretch the lobster out full length on the chopping board. With a sharp knife, split the lobster shell in half down the middle.
With the handle of a spoon or fork, lever out the tail meat in a single piece. Repeat with the other side of the tail.
Scoop out the meat from the head (including any red or green 'coral' or any brown meat). If there's a black line running down the outside of the tail, remove it with the tip of a knife.
Heat the olive oil in a large, heavy-bottomed pan. Chop the lobster tail meat into bite-sized pieces, but keep the claw pieces whole.
Add the lobster shells to the pan with the hot oil and fry for a minute or two.
Add the garlic to the pan and fry until it just begins to colour.
Add the lobster meat to the pan and season to taste with sea salt. Stir well.
Add the cherry tomatoes and the white wine to the pan and add half of the torn basil leaves and cook briefly.
Add the pasta to the pan and, using tongs, stir it into the sauce to warm it through thoroughly. Add the remaining basil leaves at the end of cooking.
Garnish with lemon wedges and a few more basil leaves before serving.