Heat olive oil in a medium pot over medium heat and saute onions until golden brown. Add garlic and saute for 1 minute.
Add cabbage and potatoes to the pot and saute for 1 minute. Add tomatoes and vegetable broth and bring to a simmer. Cook until the cabbage and potatoes are tender, about an hour.
Add in lemon juice, sugar, salt & pepper.
Ladle into a bowl and garnish with dill and sour cream.