Cook the pasta according to the package directions. Reserve 1 cup of pasta water before draining. Return it to the pot.
Make the sauce:
In a medium bowl, combine the ricotta, olive oil, grated cheese, lemon zest, lemon juice, red pepper flakes, and salt. You'll want to mix this while the pasta cooks, so you can combine it immediately after returning the pasta to the pot, when it's hot.
Combine:
Add the ricotta mixture to the pasta along with ½ cup of reserved pasta water. Use kitchen tongs (if using spaghetti) or a spoon to toss and combine, adding a little more hot pasta water if needed.
Serve:
Divide the pasta, drizzle a little fresh olive oil over the tops, and sprinkle with additional Pecorino or Parmesan.