Sauté chopped onion with olive oil and salt, until translucent, about 5-6 minutes over medium high heat in a large pot.
Add garlic and stir until fragrant, about 30-60 seconds.
Add celery and carrots and sauté 2-3 minutes.
Add broth and chicken breast to pot, bring to a boil and cover. Cook until chicken reaches an internal temperature of 165 degrees, about 10-12 minutes.
Remove chicken breast. Shred chicken and return to pot.
Add noodles and boil until al dente, about 6-7 minutes more.
Remove from heat and add lemon juice and zest. Taste and add more salt if needed. Serve hot!