In a large saucepan over medium-high, toast the barley, stirring occasionally, until lightly browned, 4 to 5 minutes. Transfer to a small bowl; set aside. In the same pan over medium-low, add the oil, carrots and ¼ teaspoon salt. Cover and cook, stirring often, until the carrots have softened, 5 to 8 minutes.

Stir in the barley, turmeric, broth and 2 cups water. Bring to a boil over medium-high, then reduce to medium-low, cover and simmer, stirring occasionally, until the barley is tender, 10 to 12 minutes.

Remove the pan from the heat and stir in the cranberries. In a small bowl, whisk together the sour cream and about ½ cup of the soup, then slowly whisk this mixture into the pan. Cover and let stand for 5 minutes. Stir in the lemon juice, then taste and season with salt and pepper. Serve topped with additional sour cream.