Cook the pasta in salted boiling water according to the package instructions. Drain, reserving 2/3 cup of the pasta water, then set aside.
In a large skillet, melt the butter over medium heat. Add the garlic and crushed red pepper flakes and cook, stirring occasionally, for 2 minutes.
Add about one-fourth of the cooked pasta to the pan, followed by one-fourth of the spinach, one-fourth of the Parmesan, one-fourth of the lemon juice and one-fourth of the lemon zest, stirring all the time until the spinach has wilted, about 1 minute. Continue this process of adding the ingredients in quarters, with additions of pasta water as needed if the mixture becomes too dry, until the pasta, spinach, Parmesan, lemon juice and lemon zest have all been added.
Sprinkle over more Parmesan and season with freshly cracked black pepper. Toss until everything is well coated. Taste and adjust the seasonings, as needed.