Cook the beets for 30 minutes in salted water. Then peel and cut into thin slices. Rinse and trim the scallions and cut into thin rings. Peel the oranges with a sharp knife, taking care to remove the white skin, then detach the segments along the natural partitions in the fruit.
Save orange juice that results while cutting the segments, then juice the remaining orange after cutting. Mix the orange juice with lemon juice, season with salt, and pepper and mix in the oil. Leave 12 orange segments whole, halve the remaining pieces and mix with beets, scallions, and the dressing. Serve garnished with whole orange slices.