Heat olive oil in a large pot over medium heat.
Add diced onion, carrots, and celery to the pot and sauté for 5-7 minutes until vegetables are tender.
Add minced garlic and cook for an additional 1 minute until fragrant.
Pour in the chicken broth and bring the mixture to a boil.
Reduce heat to low and add shredded cooked chicken, dried thyme, dried parsley, salt, and black pepper.
Simmer the soup for 15 minutes to allow flavors to meld.
Remove the pot from heat and stir in the lemon juice.
Allow the soup to cool slightly, then divide the spiralized zucchini evenly among 4 clean, wide-mouth jars.
Ladle the hot soup over the zucchini noodles in each jar, leaving about 1 inch of headspace at the top.
Seal the jars with lids and refrigerate for up to 3 days.
To serve, heat the contents of a jar in a pot or microwave until warmed through, stirring gently to combine the zucchini noodles with the soup.