Simmer the cranberries and water in a covered stainless steel pan until they are very tender, about 10 minutes. Strain the cranberries, reserving the juice. Process the berries in a food processor or blender with just a bit of the juice until they are very smooth. Stir in the remaining juice, sugar and lemon juice. Refrigerate until chilled, then freeze in an ice cream maker if you have one, or put into a somewhat flat pan or dish and freeze, stirring so a nice texture is achieved. Also, when it's quite frozen, you can transfer to a chilled dish and whip until it gets light and fluffy and sherbet-like, and then refreeze. Serve with an ice cream scoop in chilled dishes.

Very refreshing with a rich meal.