Rinse the lemon, then peel it. Combine the water and sugar in a small saucepan and cook over medium-high heat, stirring, until the mixture comes to a boil and the sugar has dissolved. Add the lemon peel, lower the heat, and simmer for 5 minutes. Let cool to room temperature. Strain the syrup through a fine-mesh sieve, then refrigerate until chilled.

Put the yogurt and honey in a bowl, add the chilled syrup and stir well. (You can also do this in a blender, but we just stirred by hand.) Pour a bit of the yogurt mixture into each of the popsicle molds, to a height of about ¾ inch.  Freeze until the mixture begins to set, about 40 minutes.

Next divide the blackberries among the popsicle molds, then pour in the remaining yogurt mixture, dividing it evenly among the molds. Snap on the lid of the molds and freeze until solid, 3 to 4 hours.