Preheat the oven to 400 degrees F and line a large baking sheet with parchment paper or foil.
Place the trimmed asparagus on the baking sheet. Drizzle with 2 tablespoons of the olive oil and sprinkle with the salt. Toss to coat, then spread the asparagus into a single layer on one side of the pan.
Lay the salmon fillets on the other side of the baking sheet. Drizzle the remaining tablespoon of olive oil over the salmon and rub it in.
Sprinkle the lemon pepper seasoning evenly over the salmon. Add the lemon zest on top of the fillets as well.
Squeeze the lemon juice over both the salmon and the asparagus.
Bake for 12 to 15 minutes, until the salmon flakes easily with a fork and the asparagus is tender.
Remove the pan from the oven. Serve the salmon and asparagus with lemon slices and a sprinkle of fresh parsley.