Put beets in a pot with water. Add salt, sugar and vinegar (vinegar preserves the beets’ bright red color). Bring to a boil, then simmer for 40 minutes.
Remove beets from the pot, reserving the broth. Put both aside to cool.
While the broth and beets are cooling, coarsely chop potato, eggs and cucumbers.
When the beets are fully cooled, coarsely grate them.
Mix together potatoes, eggs, cucumbers, scallions, dill, and beets.
When the beet broth is cool, squeeze the lemon juice into it, add previously mixed ingredients, and stir thoroughly.
Soup is served cold with a dollop of sour cream.