Heat oil in a large pot over medium heat. Cook and stir onions in hot oil until transparent, about 5 minutes. Add tomatoes and tomato sauce, using a spoon to slightly break up whole tomatoes. Season with 1 1/2 teaspoons salt and 1/4 teaspoon pepper. Cover and simmer for 20 minutes, stirring occasionally.

Stir in cabbage. Cover and simmer until cabbage is tender and mixes easily with tomatoes, about 1 hour.

Meanwhile, place ground beef, onion, eggs, water, rice, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper in a mixing bowl. Mix together with hands until thoroughly blended. Add additional rice if mixture is too moist. Form into golf ball-sized meatballs and place on a plate; refrigerate for 20 minutes to firm.

Place meatballs on the surface of tomato mixture. Cover and simmer over medium heat until meatballs are firm and cooked through, about 15 minutes. Gently stir meatballs into tomato mixture. Cover the pot and continue to simmer for 45 minutes more.

Stir in lemon juice and taste for seasoning, adding additional lemon juice if needed. Stir in raisins and honey. Add brown sugar a little at a time, tasting after each addition. Cook stew over medium heat for 15 minutes more.