In a small saucepan, combine the water and granulated sugar. Place over medium heat and stir consistently until the sugar is completely dissolved, forming a simple syrup. Once dissolved, remove the saucepan from heat and allow it to cool slightly at room temperature.
In a blender, combine the fresh raspberries, freshly squeezed lemon juice, grated lemon zest, and the cooled simple syrup. If you're looking for an added flavor dimension, incorporate the vanilla extract at this stage.
Blend the mixture on high speed until it becomes a smooth and uniform texture. If you prefer some raspberry bits in your popsicles, you can pulse the mixture a few times to maintain a bit of texture.
To remove the seeds, strain the blended mixture through a fine mesh sieve into a large bowl, pressing down on the solids with a spatula or the back of a spoon to extract as much liquid as possible. Discard the raspberry seeds left in the sieve.
Carefully pour the smooth, strained raspberry lemonade mixture into popsicle molds, filling each mold about three-quarters full to allow space for expansion as they freeze.
For a decorative swirl effect, take a teaspoon of the leftover raspberry puree and lightly swirl it into each popsicle mold using a skewer or a small spoon. This creates an enticing visual element.
Insert the popsicle sticks into the molds and transfer them to the freezer. Freeze for a minimum of 6 hours, or until the popsicles are completely solid.
To remove the popsicles from the molds, hold them under warm running water for a few seconds. This will help loosen the popsicles from the mold, making it easier to pull them out gently without breaking.
Notes
Serve on a decorative platter with fresh raspberries and lemon slices.