In a small bowl, whisk together soy sauce, brown sugar, water, and vegetable oil until sugar is dissolved.
Place fish in a large re-sealable plastic bag with the soy sauce mixture, seal, and turn to coat. Refrigerate for at least 2 hours.
Preheat grill for medium heat. Lightly oil grill grate. Place salmon on the preheated grill, and discard marinade. Sprinkle with lemon pepper. Cook salmon for 6 to 8 minutes per side, or until the fish flakes easily with a fork. Do not over cook!