Set Instant Pot to sauté function and allow it to heat. Add oil once the cooker is hot.
Salt and pepper both sides of the chicken, then sear both sides of the chicken in the pot for 2-3 minutes per side. This will likely need to be done in batches. Once chicken is seared, remove from pot and set aside.
After all chicken is seared, add more oil to the pot if needed, then add onion, carrots and celery. Sauté for 3-4 minutes, until beginning to soften. Add garlic and cook one minute more, until fragrant.
Cancel sauté function. Add herbs (thyme, parsley, oregano, dill) and rice; stir to evenly distribute through the vegetables. Place seared chicken on top of the evenly distributed vegetables and rice, then pour chicken broth over everything. Do not add lemon juice at this step.
Close the lid of the Instant Pot and set the vent to sealing. Pressure cook on high for 10 minutes. (Be aware that while this means 10 minutes of active pressure cooking, the cooker will take time to come to full pressure– possibly 15 minutes or more– before beginning to count down cook time).
Once the Instant Pot finishes the cook time, allow the pressure to release naturally for 5 minutes. Then release the pressure manually by turning the pressure knob away from sealing. Watch out for hot steam!
Once the pressure releases entirely, remove the chicken into a bowl and shred it into bite-sized pieces with two forks. Be careful, it will be very hot!
Return the shredded chicken to the pot and add the lemon juice, stirring to integrate. Allow the soup to sit on the warm setting for 5 minutes to let flavors distribute, then serve. This soup is delicious topped with a bit of shredded Parmesan cheese.