Dissolve 3 tablespoons salt in 8 cups water in a bowl. Add lingcod; let sit at room temperature for 30 minutes.

Discard salt water brine. Rinse fish; pat dry with paper towels. Season on one side with salt and black pepper.

Preheat the oven to 400 degrees F (200 degrees C).

Cut lemon in half lengthwise. Cut one half into wedges; set aside. Zest other half; set zest aside. Juice zested half into a small bowl.

Melt 1/4 cup butter in a skillet over medium-high heat. Add fish; cook until golden brown, about 5 minutes per side. Transfer to a baking dish; pour lemon juice over top.

Combine bread crumbs, Parmesan, lemon-pepper seasoning, and lemon zest in a bowl. Spread topping over fish, then dot with 1/4 cup butter pieces.

Bake in the preheated oven until bread crumb topping is golden brown and fish flakes easily with a fork, 15 to 20 minutes. Serve with lemon wedges.