In a small saucepan over medium heat, combine persimmons, sugar, water, lemon zest, and star anise When mixture boils, reduce heat to a low heat, simmer and steep for 15 minutes. Remove zest and star anise and puree mixture using a stick blender or regular blender, and funnel into a container with a lid. Chill. Syrup will keep for 1 week sealed in the fridge. Makes about 1½ cups syrup.