Bring peaches and sugar to a gentle simmer in a medium saucepan over medium heat. Cover, and cook, stirring occasionally, until peaches are soft, about 20 minutes. Let cool 10 minutes. Puree peaches and their syrup in a food processor. Pass through a medium sieve into a bowl; discard solids.
Whisk together corn syrup, lemon juice, and salt, and pour into peach puree. Whisk in buttermilk and milk. Cover, and refrigerate 30 minutes.
Freeze in an ice cream maker according to the manufacturer's instructions, until thick and creamy, 35 to 45 minutes. Transfer to an airtight container.