Cook the pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until translucent.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the diced tomatoes (with their juices), heavy cream, dried basil, and dried oregano. Stir well and bring to a simmer.
Season the sauce with salt and pepper to taste. Let it simmer for about 5-7 minutes, allowing it to thicken slightly.
Gently fold in the chopped lobster meat and cook for an additional 2-3 minutes until heated through.
Add the cooked pasta to the skillet, tossing to combine. If the sauce is too thick, gradually add reserved pasta water until desired consistency is reached.
Stir in the grated Parmesan cheese until melted and well combined.
Serve immediately, garnished with fresh basil leaves.