Portion salmon into two 8-ounce fillets if not already portioned; pat dry with paper towels on all sides.
In a small bowl, combine olive oil; rub the oil evenly over both sides of each fillet.
Season both sides of the salmon generously with coarse salt and freshly cracked black pepper.
Preheat the grill to high (about 450–550°F / 230–290°C). Clean the grates with a grill brush.
Oil the grill grates by rubbing a kitchen towel soaked in oil over the grates using long tongs to prevent sticking.
Place the salmon flesh-side down on the hot grill and cook undisturbed for 4 minutes.
Gently flip the fillets using a spatula and/or tongs and cook for an additional 2–3 minutes, until the internal temperature reaches about 125°F for medium doneness.
Remove the salmon from the grill, drizzle or brush with melted butter and lemon juice, and let rest for 2–3 minutes before serving.