Mix the blueberries and sugar in a bowl. Squeeze the lemon juice on top and mix well until the juice and sugar have formed a thick paste.
Let the blueberries macerate in the sugar and lemon juice for about an hour or so. The sugar will have melted and the blueberries exuded ample juice.
Transfer the blueberries and their juices to a saucepan and bring them to a gentle simmer. Continue simmering until the blueberries begin to burst their skins and the liquid thickens to form a kind of light caramel.
Turn off the heat, add the heavy cream and mix. Taste the mixture and stir in more sugar if you feel it needs it. Let the mixture cool completely.
Place the blueberry and cream mixture in a blender, along with the Greek yogurt if using. Whiz everything together until you have a perfectly smooth, beautifully lavender "smoothie".
Pour the blueberry smoothie into an ice cream maker and freeze, following your machine's instructions.
Serve when ready or, if you like a firmer texture, transfer to the freezer for an hour or so before serving.