Preheat the grill to medium heat or the oven to 400°F.
In a medium bowl, mix together the herbs, 2 tablespoons of olive oil, lemon pepper, and the zest and juice of one lime.
Place each salmon fillet, along with 4 pieces of asparagus, on a piece of aluminum foil large enough to completely cover them, leaving extra space to create a sealed pouch.
Divide the herb mixture evenly among the salmon fillets. Using a brush or spatula, spread the herb mixture over the fillets.
Slice the remaining lime and place the slices on top of each fillet.
Drizzle the remaining olive oil over the asparagus.
Wrap each salmon fillet in the foil, bringing the edges together to seal. Fold the edges tightly, making a ½-inch fold, then fold again to ensure a secure seal.
Place the foil packets on the preheated grill and cook for 13-15 minutes, or place the packets on a baking sheet in the 400°F oven and bake for 15-20 minutes. The salmon is done when it flakes easily with a fork or when it registers 145°F on an instant-read thermometer.
Garnish with any remaining herbs and serve.