Stir together lemon juice, lemon zest, soy sauce, brown sugar, garlic and olive oil in a 9x13-inch glass baking dish until sugar is dissolved, about 2 minutes. Place fish flesh side down in mixture and refrigerate for 30 minutes.
Preheat an outdoor grill for medium-high heat and lightly oil grate.
Place salmon on preheated grill and discard marinade.
Cook salmon until fish flakes easily with a fork, 6 to 8 minutes.