Cook the Spaghetti: Bring a large pot of water to a boil, then add the salt.
Add the spaghetti and cook according to the package instructions until al dente (usually about 8-10 minutes). Reserve about 1 cup of pasta water, then drain the spaghetti.
Make the Sauce: In a medium pot over medium heat, melt the butter.
Add the heavy cream and cook for about 2-3 minutes, stirring occasionally, until slightly thickened.
Stir in the lemon juice and lemon zest. (To prepare the zest, use a grater to remove the yellow skin of the lemon, avoiding the bitter white pith. For juicing, cut the lemon in half and use a juicer or squeeze by hand to extract the juice.) Season with ground pepper to taste.
Combine Pasta and Sauce: Add the drained spaghetti to the pot with the sauce. Toss to coat the pasta evenly.
If the sauce is too thick, add the reserved pasta water a little at a time until you reach your desired consistency.
Add Cheese and Parsley: Remove the pot from the heat and stir in the grated Parmesan cheese until well combined and creamy.
Fold in the chopped parsley.
Serve: Plate the lemon spaghetti and garnish with additional Parmesan cheese and fresh parsley.
Serve immediately, enjoying the fresh flavors!