In a large saucepan, combine rice, water, brown sugar, butter, cinnamon, salt and lemon zest. Bring to a boil. Reduce heat; cover and simmer until rice is tender and water is absorbed, about 15 minutes.
Stir in milk, condensed milk, coconut milk, raisins and vanilla. Bring to a boil. Reduce heat; simmer, uncovered, until thick and creamy, 20-25 minutes, stirring frequently. Discard cinnamon sticks. Sprinkle coconut over pudding and if desired, mango. Serve warm or chilled.