Chop the onion; slice the carrots and celery; mince the garlic.
Set Instant Pot to Sauté and warm the oil until shimmering.
Cook onion, carrots, and celery, stirring, until softened, about 4 minutes.
Stir in garlic and thyme; cook 30 seconds until fragrant.
Add chicken, broth, salt, and pepper; scrape up any browned bits.
Lock the lid and set to High Pressure for 10 minutes.
Let pressure release naturally for 5 minutes, then quick-release remaining steam.
Transfer chicken to a board and shred with two forks.
Return shredded chicken to the pot and switch back to Sauté.
Stir in egg noodles; simmer until tender, 5 to 6 minutes.
Turn off heat; stir in lemon juice and parsley. Adjust seasoning and serve.