Have ready a popsicle mold that makes 10 regular sized popsicles
Combine the water and sugar in a small saucepan.
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.
Add the yogurt and honey to the chilled syrup and stir until thoroughly combined.
Put a bit of the yogurt mixture into each of the molds, to a height of about 1/2 inch. Freeze until the mixture begins to set, about 40 minutes.
Divide the mashed banana and the mashed raspberries among the molds, alternating with the yogurt mixture, dividing it evenly among the molds.
Adjust the lid and add the wooden popsicle sticks. Freeze until solid, 4 1/2 to 5 hours.
To loosen the popsicles, run the popsicle mold under luke-warm water for 20 to 30 seconds.