Remove the 10.5 oz. package of frozen cauliflower rice from the freezer and set it on the counter to begin thawing while you prepare the other ingredients.
Trim any excess fat from the 4 chicken breasts. Cut each breast lengthwise into 2 or 3 strips.
Finely chop the 1 small onion, 2 small carrots, and 1 cup chopped celery.
Set the Instant Pot to SAUTÉ (High). Add 1 T butter and melt.
Add the chopped onion, carrots, and celery to the pot and cook 2–3 minutes, until they begin to soften.
Stir in 1 tsp Italian Herb Seasoning, 1/2 tsp ground sage, 1/2 tsp ground thyme, and salt and fresh-ground black pepper to taste. Cook 1 minute to bloom the herbs.
Add 8 cups chicken broth, the 3 T chicken soup base, and the chicken breast strips to the pot. Secure the lid and set the pressure valve to SEALING. Set to MANUAL (High) for 6 minutes.
When the cook time ends, let the Instant Pot natural release for 10 minutes, then carefully move the valve to VENTING to release any remaining pressure. Open the lid.
Remove the cooked chicken pieces to a cutting board and set the Instant Pot to SAUTÉ (Low).
Add the frozen (partially thawed) cauliflower rice to the pot and cook at SAUTÉ Low for at least 5 minutes, stirring occasionally, until heated through and tender.
While the cauliflower rice cooks, shred the cooked chicken into bite-size pieces.
Add the shredded chicken back to the soup and cook about 3 more minutes to heat through.
Turn the Instant Pot off. Stir in 1/4 cup basil pesto and 2 T fresh-squeezed lemon juice. Taste and adjust salt and pepper if needed.
Serve immediately.