Cook the fettuccine according to package instructions until al dente, then drain and set aside.
In a large skillet, heat olive oil over medium heat. Add minced garlic and sauté until fragrant, about 1 minute.
Add the cherry tomatoes to the skillet and cook until they soften, about 3-4 minutes.
Pour in the heavy cream and bring to a simmer while stirring gently.
Stir in grated Parmesan cheese until melted and well combined.
Fold in the cooked lobster meat and let it warm through for 2 minutes.
Add the pasta to the skillet along with the chopped basil, lemon juice, and toss to combine.
Season with salt and pepper to taste, adjusting as necessary before serving.
Serve immediately, garnished with additional basil and Parmesan if desired.