Stir the peaches, sugar, and lemon juice in a medium saucepan. Bring to a boil over high heat, reduce the heat to medium, and simmer, stirring frequently, until the mixture is thick and syrupy, 10 to 15 minutes. Most of the peaches will have broken down, with some softened chunks remaining.

Transfer the mixture to a blender and blend until smooth. Add the Prosecco and blend briefly to incorporate it. Let the mixture cool to room temperature and then refrigerate until cold.

Divide the mixture among ten 3-ounce pop molds or wax-lined paper cups and freeze until just barely set, about 1-1/2 hours. Insert craft sticks and freeze until firm, at least 6 hours more. When ready to serve, unmold or peel off the paper cups.

The pops can be frozen for up to 3 days.