Bring a large pot of well-salted water to a boil.
Add the pasta and cook until just shy of al dente according to package directions.
In the last 3 minutes of cooking, add the chopped rapini to the same pot. Reserve 1/2 cup of the pasta water, then drain the pasta and rapini together.
While the pasta cooks, heat 1 tablespoon of olive oil in a large skillet over medium heat.
Add the sausage and cook, breaking it into small pieces, until browned and fully cooked through. Transfer the sausage to a plate and set aside.
In the same skillet, add the remaining olive oil. Stir in the garlic and red pepper flakes and cook for about 30 seconds, just until fragrant.
Return the sausage to the pan, then add the drained pasta and rapini.
Toss everything together over medium heat, adding a splash of reserved pasta water as needed to loosen and create a light sauce.
Remove from heat and stir in the Parmesan, lemon zest, and lemon juice.
Season with salt and black pepper to taste. Serve immediately with additional Parmesan on top.