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 softened.
Add minced garlic and cook for an additional 1 minute until fragrant.
Pour in the chicken broth and bring to a boil.
Reduce heat to medium-low and add shredded cooked chicken, dried thyme, dried parsley, dried rosemary, salt, and black pepper.
Simmer the soup for 20 minutes to allow flavors to meld.
While the soup simmers, spiralize the zucchinis and set aside.
Once the soup has simmered, remove from heat and stir in lemon juice.
Allow soup to cool slightly before assembling jars.
Divide spiralized zucchini noodles evenly among 4 clean 1-quart mason jars.
Ladle the hot soup evenly over the zucchini noodles in each jar, leaving about 1 inch of headspace.
Seal jars with lids and refrigerate for up to 4 days.
To serve, heat the soup jar contents in a microwave-safe bowl or pour into a pot and warm on the stove until heated through.