In a blender container, combine all ingredients and blend until smooth. If the mixture is very thick, add cool water, a tablespoon at a time, until it reaches a thick but pourable consistency.
Taste and adjust the flavors: a little more lime or sugar, as desired. Freezing will mute the flavors so feel free to add in a pinch more of everything. Blend to combine. This yields about 2 cups of puree; number of popsicles will depend on the size of your molds.
Pour the mixture into a popsicle mold, place the handles, and freeze until firm, at least 4 hours.