Bring a large pot of salted water to boil.
Zest and juice 1 lemon (you should have about 1 tablespoon zest and ¼ cup juice) and place in a small bowl. Cut the remaining ½ lemon into thin half moons and remove the seeds. Set aside.
Cook the spaghetti until al dente, about 8 to 10 minutes. Drain the pasta, reserving 1 cup of cooking liquid.
Return the spaghetti to the pot, along with the lemon juice and zest, the butter, Parmesan, and ½ cup of the pasta water. Stir gently to combine, adding in additional pasta water if needed. Add in the red pepper flakes, prosciutto, arugula, and lemon slices. Toss gently until the arugula just begins to wilt. Season with salt and pepper (if desired) and serve immediately.
Garnish with additional grated Parmesan.