Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Place the salmon on the prepared baking sheet. Smear the salmon on both sides with the olive oil (make sure to grease the bottom of the salmon to prevent it from sticking to the pan). Spread the mustard all over the top and sides of the salmon in an even layer. Sprinkle with 1 tablespoon of the dill. Sprinkle with the salt and pepper and place the butter on top of the salmon. Put the lemon halves face-down next to the salmon on the baking sheet. Bake the salmon for about 20 minutes, until it’s just cooked through.
Transfer the salmon to a platter. Use tongs to squeeze the lemon halves over the salmon. Garnish with the remaining 1 tablespoon dill.