Heat 2 tablespoons oil in a large saucepan over medium heat. Add 1 cup onion and the sliced carrot; cook, stirring occasionally, for 2 minutes. Add minced garlic; cook, stirring occasionally, for 1 minute. Add 4 cups cabbage, 1 teaspoon each turmeric, paprika, dill and salt and ¼ teaspoon pepper; cook, stirring occasionally, for 2 minutes. Add 4 cups broth and the rinsed beans; increase heat to high and bring to a boil.
Reduce heat to maintain a lively simmer and cook, partially covered, until the vegetables are tender, 12 to 15 minutes. Remove from heat and stir in 2 tablespoons lemon juice.
