Pour the water into a small saucepan and bring it to a simmer. Add the sugar and whisk until dissolved completely.
Remove the pan from the heat and allow the simple syrup to cool a bit. Then stir in the lime juice and lime zest.
Pour the popsicle base into the popsicle molds. (see note) Place the top of the molds in place and add popsicle sticks. This may vary based on the type of popsicle mold you have.
Freeze for 5 hours or overnight. If needed, run the popsicle mold cavity under warm water to help release the popsicle.
Notes
I usually transfer the popsicle mixture into a spouted glass measuring cup to make pouring it into the molds easier. You'll need about 4 limes for juicing and 1 lime zested.