In a saucepan set over moderate heat, combine the sugar and water, bring mixture to a boil, and simmer, stirring, for 3 minutes, or until clear. Transfer to a bowl and let cool. In a food processor or blender puree the strawberries with lemon juice, to taste. Add strawberry puree to sugar syrup and stir to combine. Transfer mixture to an ice cream freezer and freeze according to manufacturer's instructions. Or freeze in cube trays.