In a small saucepan, combine the water and brown sugar. Bring to a boil and boil vigorously for 5 minutes. Remove from heat and combine with the pomegranate juice, blood orange juice, lemon juice and cinnamon. Cover and refrigerate overnight.
Process the mixture in an ice cream maker according to the manufacturer's instructions. It should take about 20 to 25 minutes to freeze up and get nice and slushy. Scoop into freezer-safe container. Freeze for at least 3 hours or up to several days.
Notes
When ready to serve, you'll likely need to take your sorbet out of the freezer and let it sit at room temperature for a few minutes until it's soft enough to scoop