For the mustard butter: With a rubber spatula, mix together the butter, both mustards, lemon zest and salt in a small bowl. Form into a 1-inch log on a large piece of plastic wrap and wrap tightly. Refrigerate for at least 4 hours.
Preheat the grill to medium high.
For the salmon: Sprinkle the salmon fillets with the salt and rub with the oil. Place on the hot grill, flesh-side down, and cook undisturbed for 4 minutes. Using a fish spatula, flip the salmon and cook for an additional 4 to 5 minutes or until cooked to your liking. Remove the salmon to a platter. Unwrap the mustard butter and slice thinly. Place a few slices on each fillet. Cover the fillets with foil to keep warm while preparing the lobster.
For the lobster: Sprinkle the lobster tails with the salt and drizzle with the oil. Place on the grill, meat-side down, and cook for 3 minutes or until golden brown. Flip the tails and top with a few slices of mustard butter. Finish cooking for an additional 4 minutes or until the meat is opaque and just cooked through. Add the lobster to the platter with the salmon and serve with additional mustard butter on the side.