Add onion, carrots, celery, garlic, broth, lemon zest, oregano, thyme, bay leaf, salt, pepper, and chicken to the slow cooker.
Cook on Low 6–7 hr or High 3–4 hr, until chicken is tender.
Remove chicken, shred, and return to the pot.
Turn to High; add orzo and cook 10–15 minutes until al dente.
Remove bay leaf. Stir in lemon juice, dill/parsley, and spinach to wilt. Season to taste.
Avgolemono option: On Warm, whisk 2 eggs with 1–2 tbsp lemon juice. Slowly whisk in 1–2 cups hot broth to temper; stir back into soup. Do not boil.
Notes
For best leftovers, cook orzo separately and add to bowls.
Dairy option: stir in 1/2–3/4 cup evaporated milk on Warm for a lightly creamy finish.
Add extra broth if soup thickens on standing.