Season salmon fillets with lemon pepper, garlic powder, and salt.
Stir soy sauce, brown sugar, water, and vegetable oil together in a small bowl until sugar is dissolved. Place fish in a large resealable plastic bag; add soy sauce mixture, seal, and turn to coat. Refrigerate for at least 2 hours.
Preheat an outdoor grill to medium heat and lightly oil the grate.
Place salmon on the preheated grill, and discard the marinade. Cook salmon until fish flakes easily with a fork, about six to eight minutes per side. Yields six servings.