Bring a large pot of salted water to boil. Cook pasta according to package instructions. Drain, reserving 1 cup of pasta water.
In the meantime, heat olive oil and butter in a large skillet over medium heat. Add garlic and red pepper flakes; cook and stir for about 30 seconds. Remove from heat.
After you have drained the pasta, set skillet with the garlic mixture over medium heat. Add the cooked pasta and ¼ cup of reserved pasta water; toss to coat. Cook and stir until heated through. If it seems too dry, add more pasta water.
Remove pasta from heat. Add and stir in lemon zest and juice, and parsley. Season to taste with salt and pepper. Serve the dish with grated parmesan cheese on top and enjoy.