Combine water, chicken thighs, and bay leaves in a large stock pot; bring to a boil, reduce heat to low, place a cover on the pot, and cook at a simmer until the chicken is tender, about 30 minutes.
Remove chicken to a cutting board to cool. Remove and discard bones, skin, and fat from chicken. Cut remaining meat into bite-sized pieces.
Cool broth until the fat congeals on the surface. Skim and discard fat.
Return soup to heat; add carrots, celery, onion, pearl barley, bay leaves, chicken bouillon, poultry seasoning, sage, salt, and black pepper. Bring the soup to a boil, reduce heat to low, place cover on the pot, and simmer until the barley is cooked and the vegetables are tender, 60 to 90 minutes. Stir lemon juice into the soup just before serving.
