Put the ginger, lemon grass, sugar and water into a small, heavy-based saucepan and simmer for 5 minutes. Remove from the heat and allow to cool.
Cut the papaya flesh into long wedges and put them in a bowl. Cut the mangoes and guavas into small wedges and add to the papaya with the lychees. Add 3 tablespoons of the syrup and combine carefully.
Transfer the salad to serving dishes, drizzle over some of the remaining syrup and sprinkle with the toasted coconut.