Preheat oven to 400 degrees F.
Place salmon on a baking sheet, drizzle with olive oil, and season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Bake for 14-16 minutes until salmon is cooked through.
While salmon bakes, bring a large pot of water to a boil. Add fettuccine and cook according to package instructions until al dente. Drain, reserving 1/2 cup of pasta water.
In a large skillet, melt butter over medium heat. Add minced garlic and sauté for 1 minute.
Stir in heavy cream, remaining salt, and pepper. Bring to a simmer and cook for 5 minutes, stirring frequently.
Reduce heat to low, add grated Parmesan cheese and lemon juice, stirring until the cheese melts and the sauce is smooth.
Flake the cooked salmon into large chunks. Add the salmon and cooked fettuccine to the sauce. Toss gently to combine, adding reserved pasta water a little at a time to reach desired consistency.
Serve hot, garnished with chopped parsley.