2. Wash and hull the strawberries. Puree in a blender or food proceesor until smooth. Press the strawberries through a very fine mesh strainer to remove the seeds and pulp.
3. Add half the sugar syrup to the pureed strawberries. Add a squeeze of fresh lemon juice and taste. Continue adding sugar syrup (by the tablespoon) and lemon juice until you reach the desired degree of sweetness.
4. Freeze the strawberry mixture in an ice cream maker according to the manufacturer's instructions.
5. Store in the freezer until ready to use.