For the orange granita, first pre-chill a metal bowl in the freezer.
Blend the lemon juice and cane sugar with half of the orange juice until all the sugar is dissolved. Blend in the rest of the orange juice and the zest zest.
Pour the fruit juice mixture into the chilled bowl and return to the freezer until a layer of ice, about 1 cm thick, has formed on the walls of the dish. Remove the bowl, scrape the ice from the walls, and mix with the juice. Return to the freezer. Repeat this procedure until the entire bowl is full of ice crystals and the mixture can no longer be stirred.
Pour the orange granita into glasses and serve with a spoon.