In a small bowl, combine the peaches with the lemon juice and 1/2 cup of the sugar. Stir until combined and set aside for at least two hours.
Strain the peaches through a colander and reserve any juice. If you like big chunks of peaches in your ice cream, set aside half of the peaches and chop into smaller pieces. Puree the rest.
In a medium mixing bowl, whisk together milk and remaining sugar just until sugar is dissolved.
Add the heavy cream, reserved peach juice, pureed peaches and vanilla.
Pour mixture into a prepared ice cream maker. Churn according to manufacturer's instructions.
About five minutes before mixing is completed, add the remaining chopped peaches.
You can eat the ice cream at this point. However, if you would like a firmer consistency, transfer the ice cream to an airtight freezer container and freeze for about two hours.