Bring a small pot of salted water to a rolling boil. Add the fresh pasta to the hot water and cook until al dente. Drain the pasta and set-aside.
Pre-heat a small saucepan over medium-high heat. Place the olive oil into the pan with the anchovies and chilli flakes. Cook until the anchovies dissolve into the oil. Add the shallots and garlic and continue to cook for 1 more minute, being careful not to burn the garlic. Place the capers, parsley, fresh lobster and tomatoes into the pan with the white wine. Cover and cook for approximately 4-5 minutes.
Remove the lid from the pan and add the cooked, drained pasta, toss well. Season with salt and pepper and serve in a large, oversized pasta plate. Garnish with shredded Parmesan cheese and fresh cut basil and serve.