Season both sides of the salmon with the sea salt and press in lightly. Season the tops (meat side) with the pepper. Let rest 10 minutes before grilling.
Meanwhile, in a small saucepan whisk together the butter, garlic, brown sugar and avocado oil. Cook over medium heat, until it begins to warm, stirring occasionally.
Stir in the soy sauce, smoked paprika and lemon juice. Continue cooking until it reaches a low bowl, stirring occasionally. Remove from heat.
Be sure you have a hot, clean and well-oiled grill. Place the salmon, meat side down, on the grill. Shut the lid and grill for about 2 to 2 ½ minutes (for under an inch-thick filet) or until the skin just begins to turn white around the edges. Flip over.
Grill an additional 1 ½ to 2 minutes, with the lid open.
Baste with the sauce and shut the lid for about 30 seconds. Remove from the grill and let rest a few minutes. Baste again before serving, if desired. Serve warm.