A full 24 hours before you make your frozen yogurt, place your ice cream insert into the freezer.
Add the sugar, vanilla, blueberries and lemon juice to a saucepan over medium heat and stir well. Press the berries with the back of a wooden spoon so the berries burst. When the sugar has dissolved, remove from the heat. Let cool then refrigerate until well chilled, about 2 hours.
Add the chilled berry mixture to a food processor. Pulse until smooth, then add the yogurt and continue to blend until completely mixed.
Turn your ice cream machine on and pour in the yogurt mixture. Churn until the mixture looks slushy, like soft serve, 12 to 15 minutes. Cover with plastic wrap and place in the freezer for several hours until it's scoopable.
Alternatively, for a chunkier texture, you can mash the berries with a potato masher or wooden spoon and stir in the Greek yogurt.