Prepare the following vegetables, adding them all to the same bowl: Dice 1 large yellow onion (about 2 cups) and 3 medium celery stalks (about 1 cup); peel and cut 2 medium carrots into ½-inch thick rounds (about 1 ½ cups). Mince 2 garlic cloves and set aside separately.
Heat 2 tablespoons olive oil in Instant Pot on the Sauté function. Tilt the inner pot to coat with the oil. Add the onion, celery, carrot, 1 ½ teaspoons salt, and ¼ teaspoon black pepper. Cook, stirring occasionally, until the vegetables are tender, 6 to 8 minutes. Stir in the garlic, 1 teaspoon dried thyme, and 2 bay leaves, and cook for 1 minute more. Push Cancel. Add chicken thighs or breasts, chicken stock, and 2 cups water.
Lock on the lid and make sure the Pressure Release Valve is set to sealing. Set to cook for 10 minutes on High Pressure. It will take about 20 minutes to come up to pressure. Meanwhile, coarsely chop ¼ cup parsley leaves and squeeze 2 tablespoons lemon juice.
When the cook time is up, do a Natural Pressure Release. Transfer the chicken with tongs to a clean cutting board. Remove and discard the bay leaves.
Turn Instant Pot back on to Sauté and bring the soup to a boil. Add noodles or pasta (about 4 heaping cups) and cook uncovered until just tender, about 5 minutes. Meanwhile, shred the chicken with two forks.
Return the shredded chicken to the pot and stir in the parsley and lemon juice. Serve immediately.
