Combine sugar, flour, and water in a large saucepan. Bring to a boil, stirring constantly until sugar dissolves; reduce heat, and simmer 3 minutes.
Drain cherries, reserving liquid. Add liquid and lemon juice to sugar mixture; stir well. Cool.
Place cherries in container of food processor or electric blender; process until smooth. Add to liquid mixture.
Pour mixture into freezer can of a 1-gallon hand-turned or electric freezer. Freeze according to manufacturer's instructions.