In a large pot, heat some oil over medium heat. Add the chopped onion and garlic, sautéing until they become translucent. Add the lamb pieces to the pot and brown them on all sides.
Pour in the broth, and bring the mixture to a boil. Reduce the heat to low and let it simmer. Add the carrots, potatoes, chopped tomatoes, and pearl barley (if using). Simmer until the vegetables are tender and the meat is cooked through.
Season the soup with salt and pepper to taste. Just before serving, stir in the lemon juice. Adjust the seasoning if needed. Ladle the soup into bowls and garnish with fresh chopped parsley.