Remove tops from beets and set aside for another use. Peel beets and cut in half if larger than 2 inches in diameter.
Place beets, potato, onion, broth, and tomato paste in slow cooker and cook on high heat for 4 hours or low heat for 8 hours.
Process soup in batches in a blender until smooth and return to slow cooker. Take great care when blending hot liquids. Do not fill blender canister more than half full, and make sure that the top is securely attached.
Before you are ready to serve, bury the cabbage in the puree. Cook on high, covered, for 45 minutes. Add 1/4 cup dill, vinegar and lemon juice and season to taste with salt.
In a separate bowl, mix remainder of dill with sour cream. Serve with a dollop of the sour cream in each bowl of soup and with lemon wedges.