Preheat the oven to 375°F. Line a sheet pan with parchment paper.
Trim the tough woody ends off the asparagus. Place on a sheet pan and drizzle with 1 tablespoon olive oil and sprinkle with a big pinch of salt and pepper. Toss to coat, then push to the sides of the pan to create enough space in the center for the salmon.
Cut half the lemon into slices. Place the salmon, skin-side down, in the middle of the asparagus and drizzle with 1 tablespoon olive oil, rub it on the flesh, then squeeze the juice from the other half of the lemon all over. Season with a large pinch of salt and pepper. Place 2 dill sprigs on top of the salmon then top with the lemon slices. Roast for 15-20 minutes (depending on the thickness of the salmon).
Mince the remaining dill and sprinkle over the top. Serve with tzatziki sauce.