In a large pot over medium heat, warm the olive oil. Add the onion, carrot, celery, lemon zest strips (if using), and ½ teaspoon salt. Cook, stirring occasionally, until softened, about 5 minutes.
Add the garlic, tomato paste, cumin, and fennel seeds and cook, stirring constantly, for 30 seconds.
Add the water, soy sauce or tamari, chicken, rice, and remaining 1 teaspoon salt. Increase the heat to bring to a boil, then reduce to low and simmer, covered, for 30 minutes, stirring halfway through, or until rice is tender. Transfer chicken to a cutting board or plate to let cool. Add your greens to the soup and simmer until wilted, about 2 minutes, then turn off the heat.
While the greens simmer, peel the skin off of the chicken, then shred the meat off of the bone (save your bones for bone broth!). Stir the meat back into the pot along with the lemon juice, starting with one tablespoon. Taste and add more if you’d like it more lemony. Taste and add more salt, if needed.
Serve with a drizzle of good olive oil and freshly grated black pepper.