Score bottom of peaches with an X and boil for about 10 seconds in boiling water and peel off skin. Remove peach pits. Puree peaches in a food processor or blender. Pour puree into a bowl and stir in simple syrup and lemon juice. Taste and adjust syrup or lemon juice to taste. Freeze in an ice cream maker using manufacturers instructions.
Stir water and sugar into a saucepan. Place pan over high heat and bring to a full boil. Let syrup cool before using. Store leftover syrup in a glass jar.