Using a large soup pot or Dutch oven, bring the chicken stock to a boil over medium-high heat.
Once boiling, add the onion, garlic, ginger, carrot, and celery, and lower heat down to medium. Cook uncovered until the vegetables are tender, about 15-20 minutes.
Add the cooked chicken to the soup and simmer until warmed through, about 2 minutes.
Stir in the fresh dill and lemon juice. Season with salt and pepper. Adjust lemon juice to taste, starting with 2 tablespoons.