Start with a small saucepan and add white wine and thyme. Let it come to a gentle boil, then reduce to a simmer.
Place the lobster tails inside, cover, and let them cook for about 5 minutes until the shells are red and the meat looks opaque. Once slightly cooled, cut through the shells with scissors, remove the meat, and chop it into bite-sized pieces.
In a large pot, bring salted water to a rolling boil. Cook the fettuccine until al dente, following the package instructions. Before draining, save about a cup of the pasta water—it will help you create a silky sauce later.
Heat olive oil in a skillet and sauté shallots and garlic until soft and fragrant. Reduce heat, then add heavy cream and butter, stirring as it simmers gently.
Mix in lemon zest and Parmesan until the sauce turns creamy and smooth. Season with salt and pepper to balance the flavors.
Add the drained pasta into the skillet and toss well so every strand gets coated. Gently fold in the lobster chunks, along with a splash of reserved pasta water to loosen the sauce. Finish it with a squeeze of fresh lemon juice, and garnish with basil leaves before serving.