Place leeks in a small bowl and toss with 2 tablespoons olive oil. Season with salt and pepper and set aside.
Line a rimmed baking sheet with parchment and coat with 2 tablespoons olive oil. Using a mandoline or a sharp knife, slice potatoes 1/8-inch thick. Lay them on the prepared sheet pan, slightly overlapping, so that the entire surface of the sheet pan is covered. Drizzle with an additional 3 tablespoons olive oil and season generously with salt and pepper. Top with another sheet pan and transfer to the oven. Roast for 20 minutes. Remove top sheet pan, top with leeks, and roast for an additional 30 minutes.
Meanwhile, season the salmon generously with salt and pepper. Combine mustard in a small bowl with 1 tablespoon olive oil, and spread on top of salmon. Place fillet in the center of the sheet pan, on top of potatoes and leeks. Transfer to oven and roast, 15 minutes, for medium doneness.
Remove salmon from oven and top with arugula. Dress arugula with remaining 2 tablespoons olive oil and lemon juice, season with salt and pepper, and serve.