Bring a large pot of salted water to a boil. Meanwhile, in a large, high-sided frying pan over medium heat, melt butter.
Add onion and cook, stirring, until onion is soft but not browned, about 3 minutes. Stir in cream, lemon zest and juice, 1/2 tsp. salt, and 1/2 tsp. pepper. Reduce heat to medium-low and cook until mixture has thickened slightly, 4 to 5 minutes.
Add pasta to water and cook according to package instructions.
Drain, reserving 1 cup cooking water.
Add salmon to cream mixture and stir to combine.
Pour pasta into frying pan with salmon-cream mixture and toss to coat, adding some of the cooking water as needed to moisten pasta.
Add parsley and toss to combine. Season to taste with salt and pepper.