Place carrots, celery, rice and chicken broth in Instant Pot. Cook on high pressure for 10 minutes. Let naturally release 15 minutes; release remaining pressure.
Remove cover and set Instant Pot to saute function on high. Stir in chicken. Cook until heated through.
Whisk eggs with lemon juice. Gradually whisk a ladle of hot broth into eggs. Whisk eggs into soup pot. Add spinach leaves and stir. Cook until just tender.
For more flavor, simmer fresh thyme sprig in the chicken broth before cooking carrots, celery and rice.