Chop the scallions crosswise into 1/4-inch pieces. In a small pot, combine the homemade chicken broth, scallions, rice, and cayenne pepper. Cook over medium-low heat for 5 minutes. While the soup cooks, scramble eggs in a small bowl. When the soup is warm and the onion is tender, whisk eggs into broth. Add the lemon juice; season with salt and pepper. Serves 4.