If using fresh lobster, boil in salted water for 8-10 minutes until the shell turns bright red. Remove and cool, then chop the meat. If using pre-cooked lobster, chop and set aside.
Bring a large pot of salted water to a boil. Add linguine or fettuccine and cook until al dente, about 8-10 minutes. Drain, reserving 1/2 cup of pasta water.
In a large skillet, heat butter and olive oil over medium heat. Add minced garlic and red pepper flakes, sauté for 1 minute until fragrant.
Add cherry tomatoes to the skillet and cook for 3-4 minutes until softened. Stir in chopped lobster meat and warm through for 2-3 minutes. Reduce heat and add heavy cream, simmer for 2 minutes.
Add cooked pasta to the skillet, tossing to combine. If dry, add reserved pasta water. Stir in Parmesan cheese, season with salt and pepper, and mix until creamy.