Heat the olive oil over medium heat in a large skillet. Add the sausage and brown it using a spatula to break it up as it cooks. Add the onion, garlic, thyme leaves, and salt. Once the sausage is browned, add the wine and lemon juice and stir, scraping up the browned bits off the bottom of the pan. Add the arugula and cook it down (add it in batches to avoid overfilling the pan).

Add the uncooked penne to the pan and stir. Pour enough water into the pan so that the pasta is almost covered (about 2 1/2 cups). Bring the pan to a boil and cook, stirring frequently, for about 15-20 minutes or until almost all of the liquid is absorbed and the pasta is tender. Serve with grated Parmesan cheese.