In a large pot of heavily salted boiling water, cook the spaghetti to al dente according to the package directions.
Reserve 1 cup of the pasta water (it comes in handy), then drain the pasta.
Meanwhile, in a large skillet over medium-high heat, cook the pancetta until crisped (~ 7 to 9 minutes)
Add the olive oil, then add the garlic, red pepper flakes, and black pepper and cook until fragrant (~ 1 minute)
Add the lemon juice to the skillet, then add the drained pasta. Toss to coat.
Add the cheese and toss, adding the pasta water, a couple of tablespoons at a time (the pasta water helps the cheese coat the pasta)
Add the arugula and toss until it wilts about 1 minute.
Season to taste with additional salt, lots of freshly ground black pepper, and red pepper flakes. Serve with more cheese