Special equipment: 6 rocket-shaped frozen pop molds 6 wooden ice pop sticks
Combine 1 cup water and the sugar in a small saucepan. Simmer over medium-high heat until all of the sugar dissolves. Remove from the heat, pour into a large liquid measuring cup and let cool completely.
Pour 1/2 cup of the sugar syrup in a blender. Add the strawberries, red food coloring and 1 tablespoon of the lemon juice. Blend until smooth. Let sit, stirring occasionally, until all the froth settles. Evenly divide among 6 rocket-shaped frozen pop molds. Take care to not to pour down the side of the molds or it will streak the pops; pour directly in the middle. Freeze until about halfway frozen and still slushy, about 40 minutes. Press a wooden ice pop stick into each about 1 inch from the bottom of the mold (the sticks should stand up straight in the middle of the mold). Return to the freezer and freeze until completely solid, about 40 minutes.
Meanwhile, stir the coconut milk and remaining 1 tablespoon lemon juice into the remaining sugar syrup. Divide the mixture in half and add the blue food coloring to one.
Once the red layer in the pop molds is frozen solid, pour in the white mixture, dividing evenly among the molds. Freeze until completely solid, about 45 minutes. Then divide the blue mixture among the molds and freeze until completely solid, about 45 minutes.
To serve, run the frozen molds under warm water before unmolding.
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