If using whole lobsters, cook them in abundant boiling water for 6 minutes. Cool, remove meat from tail, claws and knuckles, and chop into 1/2-inch chunks.
Bring a pot of well-salted water to a boil and cook pasta.
Meanwhile, pour olive oil in a wide skillet over medium-high heat. Add shallots and cook for 1 minute, without browning. Add garlic and red pepper and cook for 1 minute. Add tomatoes and season generously with salt and pepper. Add lobster meat, stir to coat, cook 1 minute, then turn off heat until pasta is ready.
When pasta is al dente, drain, add to skillet, and season with salt and pepper. Toss well and transfer to a warmed wide bowl or platter. Add basil, toss once more and serve immediately.