Heat the oil in a medium skillet over medium-high heat until the oil ripples, about 3 minutes. Pat both sides of the fish fillets dry with paper towels and then season them with salt and pepper.

Add the fillets to the skillet and cook, without moving, for 3 minutes. Slide a thin metal spatula underneath the fillets and carefully flip the fillets. If it seems impossible to slip the spatula beneath the fillet and the skillet, wait 30 seconds or so and try again. The fish will release when it’s ready.

Cook the fish until it springs back from light pressure, about 2 minutes. Use a spatula to transfer the fish to a platter or to 4 plates. Add the rest of the coconut oil, then squeeze the lemon juice into the skillet and, with the skillet still over the heat, use a wooden spoon to scrape up any browned bits stuck to the bottom of the skillet. Stir in the fresh herbs and spoon the sauce over the fish.