Cut the peach in half, remove the pit and dice the fruit. Put the peaches, Simple Syrup and lemon juice into a blender and puree until smooth. Strain the mixture through a fine-mesh strainer. Stir together the peach-simple syrup mixture with the peach iced tea. Pour half of the peach tea mixture into ice cube trays and freeze. Chill the remaining peach tea mixture.
To make the cocktails: Fill 4 tall iced tea glasses with the tea cubes. Divide the peach tea evenly among the glasses. Top each with Prosecco, garnish with a lemon slice and serve immediately.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month.