Heat oil in a 6-quart pot over medium heat. Cook onion and celery for 5 minutes until soft, then add broth, rice, salt and pepper.
Bring to a simmer, cover loosely and cook for 16 to 20 minutes, stirring occasionally, until rice is tender.
Stir in diced turkey and simmer gently for 5 to 7 minutes until it reaches 165°F. Reduce the heat to its lowest setting.
Whisk eggs, egg yolk and lemon juice in a bowl. Slowly whisk in 1 cup hot broth taken from the pot, adding it in a thin stream so the eggs warm gradually.
Stir the tempered mixture back into the soup. Heat gently while stirring for 2 to 3 minutes until the soup reaches 165°F without boiling, then remove from heat and serve immediately.