Cook the Lobster: Bring a large pot of salted water to a boil. Add lobster tails and cook for 6-8 minutes until shells turn bright red. Remove and let cool. Extract the meat, chop it into bite-sized pieces, and set aside.
Boil the Pasta: Cook pasta in the same pot until al dente, following package instructions. Reserve 1 cup of pasta water before draining.
Prepare the Sauce: In a large skillet, heat butter and olive oil over medium heat. Sauté garlic until fragrant (about 1 minute). Stir in heavy cream, Parmesan, and lemon zest. Let it simmer gently for 3-4 minutes until slightly thickened.
Combine: Add the chopped lobster meat to the sauce, followed by the cooked pasta. Toss gently to coat. Use reserved pasta water to adjust sauce consistency if needed.
Season and Serve: Season with salt, pepper, and fresh parsley. Serve hot with an extra sprinkle of Parmesan and a slice of lemon for garnish.