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—this helps it develop a better sear and prevents sticking. 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. I like to season the salmon generously on the flesh side since that's where most of the flavor develops when grilled.
Place the salmon skin-side up on the grill grates, arranging the lemon slices directly on the grill grates beside it—these will infuse subtle citrus flavor. Lay the asparagus spears perpendicular to the grill grates (this prevents them from falling through). Grill for 6-8 minutes without moving the salmon, allowing the skin to crisp and the flesh to cook through about halfway. 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 or a heat-safe bowl near the grill. Once melted, stir in the lemon zest, fresh lemon juice, and garlic powder until well combined. I always use freshly squeezed lemon juice rather than bottled—the acidity is brighter and makes a real difference in the sauce's flavor. 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.