Preheat a gas grill to medium-high heat or prepare a charcoal grill with a medium-hot fire.
Spray a 12- by 12-inch square of heavy-duty aluminum foil with cooking spray. Place the salmon, skin-side down, on the center of the foil. Sprinkle the salmon with salt and pepper and sprinkle the Italian seasoning and coriander over the top. Put 1 tablespoon of butter on top of each fillet and place 2 half slices of lemon on each. Wrap the salmon tightly in the foil, place on the grill, and cook for 10 minutes.
Remove the salmon from the grill and open the foil packet to allow the steam to escape. Let stand until cool enough to handle. Reserving any cooking liquid in the foil packet, transfer the salmon to a small bowl and using a fork, flake it into large pieces; discard the skin.
Meanwhile, bring a large pot of salted water to a boil and cook the linguini until al dente, according to the package instructions. Put the peas in a large mixing bowl, drain the pasta and pour it over the peas in the bowl. (The heat from the pasta will cook the peas.) Add the reserved cooking liquid from the salmon to the bowl along with the tomatoes, capers and lemon zest.
In a small bowl, whisk the lemon juice, olive oil and mustard together until thick and emulsified; pour the dressing over the pasta and toss well to coat. Add the flaked salmon and dill, and toss gently until combined. Taste and adjust the seasoning, if necessary.
Transfer the pasta to a serving platter, garnish with chopped parsley and lemon slices, and serve immediately.