Combine mustard, olive oil, lemon juice, lemon pepper, dill, black pepper, and garlic salt in a resealable plastic bag; add salmon. Gently coat salmon with the marinade. Place sealed bag in refrigerator; marinate about 2 hours.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Cook salmon skin-side down on the grill, 3 to 4 minutes. Flip and cook until fish flakes easily with a fork, or to desired degree of doneness, 3 to 4 minutes more.