Brew the espresso, and while it is still hot add the sugar and the lemon juice. Taste and add more sugar, to taste. Cool espresso mixture to room temperature.
Pour the mixture into a 13 by 9-inch pan, and set on a level shelf in the freezer. When ice crystals begin to form, approximately 30 minutes to 1 hour, remove pan from freezer and stir ice crystals. Return pan to freezer and repeat every time ice crystals form. Once all the liquid is frozen, the granita is ready.
To serve, use a large coffee cup or a martini glass. Place granita in dish and top with some fresh whipped cream.