Combine half the lemon balm leaves, water, lime zest, and sugar in a medium saucepan. Set over medium heat and bring to a boil; stirring until sugar dissolves. Cover, remove from heat, and let cool.

Thinly slice remaining lemon balm leaves. Strain sugar mixture into a 1-quart measuring cup or bowl. Add lime juice and sliced lemon balm leaves.

Pour into popsicle molds using the measuring cup or funnel and freeze until solid, about 4-5 hours. If you want the leaves to be dispersed in the popsicles, give them a stir every hour for the first 2-3 hours or until too hard to stir.