Cut open the lobster tails with kitchen scissors, remove the meat, and cut into bite-sized chunks.
Boil pasta in salted water until al dente. Reserve 1 cup of pasta water, then drain.
Heat olive oil in a skillet, sauté lobster for 2-3 minutes until opaque. Remove and set aside.
In the same skillet, sauté garlic for 1 minute. Deglaze with white wine and reduce by half. Add broth, reduce again, then stir in cream, butter, and Parmesan until smooth. Season with salt, pepper, and red pepper flakes if using. Stir in lemon juice.
Return lobster to the skillet, add pasta, and toss until coated. Add reserved pasta water as needed for creaminess.
Garnish with parsley and extra Parmesan. Serve immediately.
