Pour the cooled lemon mixture into a baking pan or dish large enough (about 9 x 13 inches) so that the mixture is not more than about 1 inch deep (it will take longer to freeze and be a bit harder to work if it is any deeper).
Place the pan in the freezer and freeze until it the granita becomes firm, but not completely solid, about 1-2 hours depending upon your freezer.
Remove the pan from the freezer and let it sit until you can break the granita into chunks with a couple of forks. Dump the chunks into a food processor and pulse until it is the consistency of snow. Serve immediately, or return the granita to the freezer until ready to serve. If it freezes very hard by the time you serve it, simply let it sit on the counter for a few minutes and work it a bit with 2 forks until soft. Serve immediately.