Add watermelon, 2 Tbsp granulated sugar and lemon juice to a blender and blend until well pureed. Skim off foam then carefully pour into 10 popsicles molds filling each about 2/3 full (try not to splash on sides, I found it worked best to let it run down the outside edge then just wipe off that part later with a damp paper towel or q-tip). Sprinkle the chocolate chips over tops then using a popsicles stick gently push down to immerse chips (push towards sides so you can see them once the freeze). Wipe sides clean as needed. Cover with the lid and insert popsicles sticks. Freeze 3 1/2 hours. During last 30 minutes of popsicles freezing, whisk together coconut milk with 1 1/2 Tbsp sugar until sugar has dissolved, chill 30 minutes (you want it to be a nice pourable consistency after chilling, not too thick. If you find that it is stir in 1 - 2 Tbsp cold water to thin. I recommend chilling it because you just don't want it warm or it will melt the watermelon layer when pouring in).
Remove popsicles from freezer, remove lid and carefully pour a scant tablespoon coconut milk into an even layer over watermelon layer (again, it works best to pour it down the outside edge then wipe clean). Clean sides as necessary. Return to freezer, uncovered, and chill 45 minutes. Meanwhile, cut tops from kiwi and use a spoon to scoop flesh from kiwi while leaving skins. Transfer kiwi to blender along with 2 Tbsp granulated sugar. Pulse until well pureed. Force mixture through a fine mesh strainer into a bowl using a rubber spatula to remove seeds (at this point I mixed int just a tiny bit of blue gel coloring because mine weren't the best shade of green, so that's optional). Chill kiwi mixture 30 minutes.
Remove popsicles from freezer and carefully pour about 1 Tbsp kiwi mixture over coconut layer. Return to freezer and chill until popsicles are solid about 2 - 3 hours.
To remove popsicles from molds, turn tray to the side and run plastic molds under warm water several seconds (don't let the water touch the kiwi portion at the top) then slowly pull from molds.