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