Add the sugar, vanilla, peaches and lemon juice to a large saucepan over medium-high heat. Stir until the sugar begins to melt, 1 to 2 minutes. Cover, reduce the heat to medium and simmer 5 minutes.
Meanwhile, add the cornstarch to a small bowl and mix with 1 tablespoon water. Remove the cover from the peach mixture and stir in the cornstarch. Keep stirring until thick, about 1 minute. Once the mixture is thickened, remove from the heat and allow to cool. Refrigerate until chilled, at least 30 minutes.
To serve, layer the yogurt and peaches in a serving glass.