Puree blueberries and raspberries in a blender or food processor until smooth. Press puree through a fine mesh strainer into a large bowl. Discard seeds.
Stir in ginger ale, corn syrup, sugar and lemon juice.
Freeze in a 1-1/2 to 2-quart ice cream freezer following manufacturer's instructions. Spoon into freezer container; cover and freeze several hours or until desired firmness is reached.