Preheat the oven to 425°F and line a large sheet pan with parchment paper or foil.
In a bowl, toss the halved potatoes with 2 tablespoons olive oil, minced garlic, salt, and pepper. Spread them in a single layer on the sheet pan.
Roast the potatoes for 15 minutes. Remove the pan from the oven and push the potatoes to one side.
Add the asparagus to the empty space on the pan and drizzle with the remaining tablespoon of olive oil. Season lightly with salt and pepper.
Place the salmon fillets on the pan. Stir together the lemon zest, lemon juice, parsley, and oregano, then brush this mixture over the salmon.
Return the pan to the oven and roast for 12 to 15 minutes, until the salmon flakes easily and the vegetables are tender.
Serve hot with lemon slices on the side.