Scrub beets; cut off all but 1 inch of stems and roots. Do not peel beets.
In a 4-quart Dutch oven combine beets, Vegetable Stock, water, onions, and salt. Bring to boiling; reduce heat. Simmer, covered, for 20 minutes. Using a slotted spoon, remove beets; cool slightly. Slip skins off beets; discard. Cut beets into large pieces. Return to Dutch oven.
Stir in sugar and lemon juice. Bring to boiling; reduce heat. Simmer, uncovered, for 10 minutes. Season to taste with salt. If desired, cover and refrigerate.
To serve, ladle the soup into bowls, placing an onion half in each bowl. Sprinkle with cabbage.