Heat the oven to 400°F. Pat salmon dry, rub with oil, season with its salt and pepper and roast on a lined sheet pan for 10 to 15 minutes until the thickest center reaches 145°F.
Meanwhile, cook tagliatelle in water with the tablespoon salt until 1 minute short of the package time. Reserve 1 cup pasta water before draining.
Melt butter in a large skillet over low heat, add cream, milk and lemon zest and simmer gently for 2 minutes. Add pasta with 1/4 cup reserved water and toss for 1 to 2 minutes until tender.
Remove from heat and stir in Parmesan gradually, loosening with more water if needed. Let cooked salmon rest for 2 minutes and flake each portion into a few broad pieces.
Divide pasta among bowls and set salmon flakes over it, spooning only a little sauce around the fish so the pieces stay intact.