In a saucepan, combine water and sugar, and bring to a boil until sugar is dissolved.

Add the diced peaches and candied ginger, and simmer for about 10 minutes.

Remove from heat and let cool.

Stir in lemon juice.

Refrigerate the mixture for at least 2 hours until thoroughly chilled.

Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions.

Transfer to a container and freeze for at least 2 hours before serving.