Cook spaghetti according to package directions until al dente. Reserve about 1 cup of pasta water before draining.
While the pasta is cooking, heat olive oil in a large skillet over medium heat. Add minced garlic and red pepper flakes and cook until fragrant, about 1-2 minutes, being careful not to burn the garlic.
Stir in the fresh lemon juice and bring to a simmer.
Add the drained spaghetti to the skillet with the sauce. Toss to coat.
Gradually add reserved pasta water, about 1/4 cup at a time, tossing until a light sauce forms and coats the pasta. Add more pasta water if needed to reach desired consistency.
Stir in the grated Parmesan cheese and chopped fresh parsley. Season with salt and black pepper to taste.
Serve immediately, garnished with extra parsley and Parmesan if desired.
Notes
This pasta is best served fresh. Leftovers can be reheated gently with a splash of water or broth.