Chop the onion finely and mince the garlic, setting both aside for sautéing.
Use a microplane or grater to zest the lemon, then squeeze out the juice into a small bowl, removing any seeds.
Heat the large pot over medium heat, then add olive oil. Once shimmering, add the chopped onion and minced garlic, sautéing until fragrant and translucent, about 5 minutes.
Pour in the chicken broth, bringing it to a gentle simmer, and add the shredded cooked chicken. Stir to combine and heat through for about 5 minutes.
Stir in the lemon juice and zest, then season with salt and pepper. Let the soup simmer gently for another 10 minutes, allowing flavors to meld and brighten.
If using greens, stir them into the hot soup and cook until wilted, about 2-3 minutes. The greens will add a fresh, tender bite.
Taste the soup and adjust seasoning if needed, adding more lemon juice, salt, or pepper to achieve your desired brightness and balance.
Serve the lemon chicken soup hot, spooned into bowls, and enjoy the warm, zesty comfort in every sip.