Add watermelon, 1½ tablespoons of sugar and lemon juice to a blender and blend until well pureed.
Skim off foam and carefully pour into about 10 popsicle moulds, filling to about ⅔ full.
Cover with the lid and insert the popsicle sticks and freeze for 3 hours. Watermelon juice separates naturally so stir it gently every 30 minutes.
Once the juice is slushed, sprinkle chocolate chips over the tops and push gently down to immerse, keeping some touching the insides of the moulds.
After three hours, whisk coconut milk and 1 tablespoon of sugar until dissolved then chill for 30 minutes. You want a nice pouring consistency after chilling, not too thick. If it thickens too much stir in 1-2 tablespoons of cold water to thin.
Remove popsicles from freezer and pour about a tablespoon of coconut milk into an even layer over the watermelon layer. Return to freezer, uncovered, and chill for at least 45 minutes. Meanwhile, peel the kiwis and transfer the fruit to the blender along with the remaining sugar. Pulse until pureed. Rub through a fine mesh strainer to remove seeds, and chill the puree for 30 minutes.
Take popsicles from freezer and top each with kiwifruit mixture, about a tablespoon each. Return to freezer and chill until popsicles are fully solid, about 2-3 hours.
To remove popsicles from moulds, turn tray to the side and run plastic moulds under warm water several seconds without letting water touch the kiwi at the top. Then slowly pull from moulds.