Combine strawberries, powdered sugar, sweetener, 1 tablespoon lemon juice, and 1/4 cup water in blender container. Purée, if too sweet, add additional 1/2 tablespoon lemon juice.
Pour into metal 8-inch square pan. Cover pan with foil and place in freezer. Freeze granita 2 hours or until slushy. Remove from freezer and stir to break mixture up into small chunks. Cover and return to freezer. Freeze 2 hours then stir to break granita up again. Cover and freeze at least 4 hours or overnight.
To serve, scrape surface of granita with large metal spoon to shave off thin pieces. Spoon into individual bowls and serve immediately.