In the saucepan combine the sugar and water. Cook over medium heat until completely dissolved. Let cool for 15 minutes.
In the blender, purée the cherries, pomegranate juice, and lemon zest with the syrup until very smooth. Pour into the bowl. Cover and refrigerate until chilled, at least 4 hours or overnight.
Churn in an ice cream freezer according to the manufacturer's directions. Transfer the churned sorbet to the plastic container. Press a layer of plastic wrap against the sorbet and seal the lid on top. Freeze until fully hardened, at least 6 hours.