Heat a tablespoon of oil in a heavy-bottomed pot over medium heat until shimmering. Add diced onion and cook, stirring occasionally, until translucent and fragrant, about 5 minutes.
Add minced garlic, grated ginger, chopped carrots, and celery to the pot. Cook, stirring often, until the vegetables soften slightly and smell sweet, about 5 minutes.
Pour in the chicken broth and bring the mixture to a gentle simmer. Stir in the rice, then cover and cook until the rice is tender, about 15 minutes, stirring occasionally to prevent sticking.
Uncover the pot, stir in shredded cooked chicken, and squeeze in the juice of one lemon. Taste and adjust seasoning with salt and pepper.
Finish by zesting a bit of lemon over the soup and sprinkling chopped fresh herbs on top for a burst of color and freshness.
Serve steaming hot, with an extra squeeze of lemon if desired, and enjoy the bright, comforting flavors in every bowl.