Bring a large saucepan of salted water to a boil. Add the green beans and cook, adjusting the heat as needed to maintain a simmer, as you cook the sauce. (Don't worry about overcooking the beans; they can simmer for 10 to 30 minutes total.)

While the beans simmer, heat the oil in a large Dutch oven over medium. Add the onion and season with salt and pepper. Cook, stirring occasionally, until the onion is soft and translucent, about 3 minutes.

Add the sausage and cook, breaking it up with a wooden spoon and stirring occasionally, until well browned and starting to stick to the bottom of the pan, about 7 minutes.

Reduce the heat to low. Stir in the fennel seeds and red pepper and cook until fragrant, just a few seconds.

Add the juice of ½ lemon and ½ cup of the cooking water from the green bean pot. Raise the heat if needed to simmer, stirring constantly, until the ragù is glossy, about 5 minutes. Add more water from the pot if necessary; the ragù should be saucy like gravy. Keep warm over very low heat.

Add the pasta to the saucepan with the green beans and cook according to package instructions.

Reserve 2 cups of the cooking water. Drain the pasta and green beans and transfer to the Dutch oven with the ragù.

Add the Parmesan and 1 cup of the reserved cooking water, stirring vigorously, until the pasta is saucy and shiny and lightly coated with sauce. If needed, stir in more water, a little at a time. Taste and add more salt, pepper, lemon juice and cheese as desired.