Fill an Instant Pot 1/3 – 1/2 of the way full with water. Place the chicken in the water. All of the chicken should be submerged in the water. Set the Instant Pot to Poultry for 15 minutes on high pressure.
Remove the chicken and shred with two forks. While the chicken is cooking, chop the vegetables. Heat olive oil over medium heat. Add the carrots, celery, and green onions. Cook for 5 minutes.
Add the garlic, broth, bay leaves, salt, and white pepper. Bring to a boil. Add the rice. Cover and reduce heat. Cook for 20 minutes until the rice is tender.
Add the shredded chicken back to the pot.
In a separate bowl, whisk together the eggs and lemon juice. Temper the eggs by slowly adding two ladles of hot broth while whisking. Add two ladles of broth to the bowl with the eggs and lemon juice. Beat with a fork to combine.
Remove the sauce pan from the heat. Add the lemon and egg mixture to the soup.
Garnish with fresh dill and serve right away. Enjoy!