Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.
In a large skillet, melt the butter and olive oil over medium heat. Add the minced garlic and red pepper flakes (if using) and sauté for about 1 minute until fragrant.
Add the chopped lobster meat and cherry tomatoes to the skillet. Cook for 3-4 minutes, stirring gently until the tomatoes begin to soften.
Add the cooked pasta to the skillet along with the reserved pasta water. Toss everything together until well combined.
Stir in the chopped parsley, lemon juice, and season with salt and pepper to taste. Cook for an additional 1-2 minutes to heat through.
Serve the pasta hot, topped with grated Parmesan cheese.