If using fresh blackberries, freeze and thaw them before adding to help draw out juices.
1. Place sugar and hibiscus flowers in heat-proof bowl, and cover with 1 1/4 cups boiling water. Stir to dissolve sugar, and cool. Strain, and discard solids.
2. Pulse blackberries in food processor until just puréed, without chopping seeds. Strain through sieve, and discard seeds and solids (you should have 3 cups purée). Stir in hibiscus syrup and lemon juice.
3. Chill in refrigerator until cold, then churn in ice cream maker according to manufacturer’s directions. Transfer to 1-quart container, and freeze.