Heat olive oil in a large pot over medium heat.
Add onion, celery, and carrots. Cook until softened, about 5–7 minutes.
Stir in garlic and cook for 30 seconds until fragrant.
Pour in chicken broth and bring to a gentle simmer.
Add the rice and cook until tender, about 12–15 minutes.
Stir in the shredded chicken and let it warm through.
In a bowl, whisk the eggs with the lemon juice until smooth.
Slowly ladle about 1 cup of hot broth into the egg mixture while whisking constantly to temper the eggs.
Gradually pour the egg mixture back into the soup, stirring gently.
Heat the soup on low until slightly thickened. Do not let it boil.
Season with salt, pepper, lemon zest (if using), and stir in fresh herbs.
Serve warm.