Heat the oil in a soup kettle over medium-high heat. Add the onion and sauté until tender, 4 to 5 minutes. Add the broth, 3 tablespoons of the lemon juice, and the chicken. Bring to a simmer, reduce the heat to medium-low, and add the pasta. Continue to simmer, partially covered, until tender, 10 to 12 minutes.
Meanwhile, whisk the remaining 2 tablespoons lemon juice into the whole eggs and egg yolks.
Transfer a ladleful of the hot broth to a small bowl. Add the spinach and dill to the soup pot. Whisk the ladleful of hot broth into the eggs, then return the egg mixture to the pot and gently heat until creamy, about 1 minute longer. Remove from the heat and adjust the seasoning, including salt and pepper to taste. Serve immediately.
Garnish with crumbled feta if available.