Preheat your oven to 400°F (200°C).
Cut two large pieces of aluminum foil, about 12 inches long each.
In a small bowl, mix together olive oil, minced garlic, oregano, salt, and pepper.
Place one salmon fillet in the center of each piece of foil. Arrange the asparagus around the salmon.
Drizzle the olive oil mixture over the salmon and asparagus. Top each salmon fillet with lemon slices.
Fold the sides of the foil over the salmon and asparagus to create a sealed packet.
Place the foil packs on a baking sheet and bake in the preheated oven for 15-20 minutes, or until the salmon is cooked through and flakes easily with a fork.
Carefully open the foil packs (watch out for steam) and garnish with fresh parsley before serving.