Heat canola oil in a large pot over medium-low heat. Add onion; cook and stir until softened, 5 to 8 minutes. Stir in spinach, mushrooms, and celery; cook until heated through, about 5 minutes. Season with oregano, salt, and pepper.
Pour chicken broth and water into the pot. Stir in rice and lemon zest. Bring soup to a boil. Reduce heat and simmer, covered, until rice is tender, about 20 minutes.