Combine the sugar, 2 cups water, and orange zest in a medium saucepan. Simmer until sugar is dissolved. Stir in the basil, orange juice and lemon juice. Let stand at room temperature to infuse for one hour, or refrigerate up to overnight.
Pour into a wide shallow container. Cover with a lid, plastic wrap, or foil. Transfer to freezer until frozen around the edges. Remove from freezer, and scrape the ice with a fork, mixing it from the edge into the center. Return to freezer. Repeat scraping and mixing process every 30 minutes or so (at least 3 times) until the entire mixture has turned into small, sequined ice flakes.
Best eaten immediately. If leaving in freezer overnight or longer, let sit at room temperature until it softens a little, then scrape it again with a fork to lighten the texture.