Preheat oven to 425°F. Place each beet on a square of foil and drizzle with some of the 2 teaspoons oil. Wrap tightly and place on a baking sheet. Roast until you can easily pierce the beet with the tip of a sharp knife, about 45 minutes. Unwrap the beets and set aside until cool enough to handle, about 30 minutes. Peel and refrigerate until chilled, about 15 minutes.
Meanwhile, reduce oven temperature to 350°. Place flatbreads on the baking sheet and brush both sides with 1 tablespoon oil. Bake the flatbreads until slightly crispy around the edges, about 10 minutes.
Combine the beets, 1 cup labneh (or yogurt), 2 tablespoons oil, lemon zest, 1 ½ tablespoons lemon juice and ¼ teaspoon salt in a food processor; process until smooth.
Toss arugula with the remaining 2 tablespoons oil, 1 ½ tablespoons lemon juice, ¼ teaspoon salt and pepper in a medium bowl. 5. Spread the beet mixture on the flatbreads and divide the arugula and smoked salmon among them. Dollop the remaining ⅓ cup labneh (or yogurt) on top.
