Preheat the oven to 390 degrees F (200 degrees C).
Lightly salt and pepper salmon fillet on both sides, and place in a 2-quart baking dish. Squeeze 1 lemon half over the salmon, then sprinkle with minced garlic and 1/2 of the butter pieces.
Bake in the preheated oven until salmon is cooked through and flakes easily with a fork, about 15 minutes.
Meanwhile, fill a large pot with lightly salted water and bring to a rolling boil. Cook fettuccine at a boil until tender yet firm to the bite, about 8 minutes.
When salmon is cooked, break apart into large chunks (it will break apart a little further when you toss it with the pasta.)
Add cooked pasta to the baking dish with the salmon. Drizzle pasta and salmon with olive oil, and add remaining butter pieces. Zest the remaining lemon half and add to the pasta, then squeeze juice from the zested lemon into the pasta as well. Add parsley, salt, and pepper.
Toss everything gently until pasta is well coated in the pan juices and everything you have added in, and salmon is evenly distributed amongst the pasta. Taste and adjust seasonings if necessary. Add a touch more butter or oil if needed, if your pasta is too dry.
