Puree the blueberries in a blender until smooth. Strain through a fine mesh sieve, pushing down with a spatula or spoon to get all of the liquid out. Discard the solids. Stir the lemon juice, water and sweetener into the blueberry puree.

Pour the blueberry mixture into a shallow baking dish and place in the freezer. Remove the dish after 30 minutes and using a fork, scrape the mixture, breaking up any icy clumps. Return the dish to the freezer. Repeat the process every 30 minutes or so, scraping it with a fork, to create a light and fluffy texture. It should take about 2 hours total.