Bring a large pot of salted water to a boil.
Add the spaghetti and cook until al dente, following package directions. Reserve ¼ cup of pasta water, then drain the pasta and set it aside.
In a large skillet over medium heat, add the reserved pasta water, lemon juice, and 4 tablespoons of the butter. Stir until the butter is melted.
Add the minced garlic to the skillet and cook for 30 seconds.
Add the cooked spaghetti to the skillet and toss to coat in the sauce.
Add the remaining 2 tablespoons of butter and kosher salt. Continue tossing until the butter is fully melted and the noodles are evenly coated. If needed, add a splash more pasta water to loosen the sauce.
Divide the pasta into warmed bowls. Top each serving with parmesan cheese, a squeeze of lemon, and a sprinkle of fresh parsley. Drizzle with a bit of olive oil, if using. Serve immediately.