Heat olive oil in a dutch oven or large soup pot over medium-high heat.
Add the onion and saute until golden, about 6 minutes.
Add the carrots, celery and garlic. Cook for 5 minutes, stirring occasionally.
Stir in the barley until well dispersed, then add the broth, chicken breasts, salt and pepper (if adding bay leaves add them here too).
Bring to a boil. Once boiling, lower the heat and bring to a simmer. Cover and poach the chicken until cooked, about 15 minutes for large breasts (check at thickest part for 165F internal temp or clear juices running through). Remove chicken breasts from the broth and set aside to cool.
Stir in the lemon juice. Cover and continue cooking until the barley is tender, about another 25-30 minutes, stirring occasionally.
Meanwhile, shred the chicken with two forks.
When ready to finish, stir in the shredded chicken. Let simmer for a few minutes to warm through and soak up flavor. Sample the soup– add salt, pepper or lemon juice paste if needed to taste. For more flavor, stir in a little roasted chicken paste.
Serve hot with fresh cracked pepper and enjoy! Also yummy topped with sour cream and served with bread to soak up the juices!