While your grill is preheating to medium-high heat, trim the asparagus ends (about 2 inches from the bottom) and pat the salmon fillet dry with paper towels. In a small bowl, combine salt, black pepper, and dried oregano. Brush the olive oil evenly over both the salmon skin and the asparagus spears, then season generously with the herb mixture on all sides.

Place the salmon skin-side up on the grill grates, arranging the lemon slices directly on the grill grates beside it. Lay the asparagus spears perpendicular to the grill grates. Grill for 6-8 minutes without moving the salmon. After 6-8 minutes, carefully flip the salmon flesh-side down and rotate or flip the asparagus spears. Continue cooking for 5-6 minutes until the salmon is opaque and flakes easily with a fork, and the asparagus is tender with light char marks.

While the salmon and asparagus finish cooking, melt the butter in a small saucepan over low heat. Once melted, stir in the lemon zest, fresh lemon juice, and garlic powder until well combined. Keep the sauce warm but don't let it brown.

Transfer the grilled salmon and asparagus to a serving platter or individual plates. Discard the grilled lemon slices or use them as a garnish if desired. Pour the warm lemon-butter sauce evenly over the salmon and asparagus, then finish with freshly chopped parsley scattered on top.