Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain the pasta.
Meanwhile, heat the olive oil in a large Dutch oven or wide skillet over medium-high heat. Add the sausage and cook until browned, about 5 minutes. Transfer to a plate using a slotted spoon; set aside.
Wipe the Dutch oven clean; add the butter and melt over medium heat. Add the garlic and cook, stirring, until slightly softened, 1 to 2 minutes. Add the chard and cook, stirring occasionally, until wilted, 3 to 4 minutes. Sprinkle in the flour and cook, stirring, until combined, 1 to 2 minutes.
Add the milk to the chard mixture and bring to a boil; cook 1 minute. Stir in the sausage, parmesan, lemon zest and a few grinds of pepper. Reduce the heat to medium low and simmer, stirring occasionally, until slightly thickened, about 6 minutes. Add the pasta to the pot and toss, adding enough of the reserved pasta water to loosen.