Combine sugar and water in small saucepan and bring to boil over high heat about 1 minute. Transfer syrup to a heatproof container and chill until cold, about 2 hours.
Puree blackberries with juices and sugar syrup in a blender until smooth. Strain into a large bowl to remove the seeds and stir in lemon juice and rose water.
Process berry mixture in ice cream maker according to manufacturer’s instructions. Transfer to a container, cover, and freeze until firm, about 6 hours.
