Bring a large pot of salted water to boil. Add rigatoni and cook until al dente. Drain, reserving about ½-3/4 cup cooking liquid. Set aside.
Meanwhile, in a heavy bottomed saucepan, heat olive oil over medium high heat. Add sausage and cook until outside browns and inside is done, about 6-10 minutes. Transfer to cutting board. Once slightly cooled, slice into ½-1 inch pieces on the diagonal.
Turn heat down a bit and add butter. Once butter has melted, stir in fennel and salt. Cook for 8-10 minutes, stirring frequently, until the fennel starts to brown. Add in shallot and garlic and cook for 1 minute. Next, stir in lemon juice and white wine vinegar, reduce heat to low, and simmer for about 1-2 minutes.
Turn up the heat to medium high and add sliced sausage back into saucepan. Add in pasta, a ¼ cup of reserved pasta water, Parmesan cheese, and thyme. Stir well to make sure everything is nicely coated. If pasta looks too dry, add an additional ¼ cup pasta water and continue to stir and cook. Adjust salt to taste and top with freshly ground black pepper before serving.