To make the syrup, combine water, sugar lemon juice, and gingerroot in a small saucepan, and heat until brought to a boil, then reduce the heat.
Simmer the syrup for about 3 minutes leaving uncovered, then remove from the heat and stir in lemon peel. Cool the syrup to room temperature and strain if desired, then pour the syrup over the melon. Stir the melon and syrup gently to coat, then cover and allow them to chill for 2 to 24 hours.
Take melon and syrup and spoon into dessert dishes to serve, and then sprinkle with coconut.