Preheat the oven to 375°F (190°C).
Lay out a large piece of aluminum foil on a baking sheet.
Place the salmon fillets in the center of the foil.
Arrange the asparagus around the salmon.
Drizzle olive oil over the salmon and asparagus.
Sprinkle minced garlic, lemon juice, thyme, salt, and pepper over the top.
Fold the foil over the salmon and asparagus to create a sealed packet.
Bake in the preheated oven for 20 minutes, or until the salmon is cooked through and flakes easily with a fork.
Carefully open the foil packet to avoid steam.
Serve immediately, garnished with additional lemon slices if desired.