To make: *Combine the peaches, 1/2 cup of the sugar, and the lemon juice in a bowl. Cover and refrigerate for 2 hours, stirring the mixture every 30 minutes.
*Remove the peaches from the refrigerator and drain the juice into another bowl. Return the peaches to the refrigerator.
*Whisk the eggs in a mixing bowl until light and fluffy, 1 to 2 minutes. Whisk in the remaining 3/4 cups of sugar, a little at a time, then continue whisking until completely blended, about 1 minute more. Pour in the cream and milk and whisk to blend. Add the peach juice and blend.
*Transfer the mixture to an ice cream maker and freeze following the manufacturer's instructions.
*After the ice cream stiffens (about 2 minutes before it is done), add the peaches, then continue freezing until the ice cream is ready.
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