Heat the vegetable oil in a large saucepan over medium-low heat. Cook the onion in the oil until it has softened and turned translucent, about 4 minutes. Stir in the raisins, apricots, lemon zest, lemon juice, and water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer 5 minutes. Add the apples, and cook about 5 minutes longer until the apples soften. Season with additional cinnamon, salt, and pepper if desired. Stir in the shredded chicken before serving.