Combine ½ cup of water and the sugar in a pot. Heat over medium heat until sugar is dissolved. Remove the simple syrup from the heat to cool.
Put the raspberries in a blender and puree. Pour the raspberry puree through a sieve (with a bowl underneath) to remove the seeds. Use the back of a spoon to help push the raspberry juice through the sieve.
Pour ¼ cup of water in the blender to get all of the raspberries out - pour that through the sieve to separate juice from the seeds.
Pour the remaining ¼ cup of water into the seeds to make sure they are cleaned. Discard the seeds.
Add the lemon juice, lemon zest and simple syrup to the raspberry juice. Stir and pour into a shallow pan. Cover with foil and put in the freezer.
Every hour, take a fork and scrape the top of the granita to form crystals. Repeat this process until the entire granita is frozen.
Use an ice cream scoop to serve. Garnish with lemon zest.