Combine mashed berries and 1 cup sugar in a large mixing bowl. Set aside 1 hour.
Press blackberry mixture through a sieve; set blackberry juice aside, and discard pulp.
Dissolve gelatin in boiling water in a large mixing bowl; stir in blackberry juice. Add remaining sugar, lemon juice, and enough water to yield 5 cups of mixture.
Pour mixture into freezer can of a 1-gallon hand - turned or electric freezer. Freeze according to manufacturer's instructions. Let ripen 1 1/2 to 2 hours before serving. Scoop into sherbet dishes, and serve immediately.
Note: Two quarts fresh blackberries, mashed, may be substituted for frozen berries.