Combine the peaches, lemon juice, and sugar in a small sauce pan over medium-high heat. Bring to boil. Reduce the heat to low and simmer for 10 minutes.
Next, transfer the mixture to a food processor or blender and pulse until smooth. Be careful, it will be hot! Cool completely before adding to ice cream base.
Make the Ice Cream Base
In a stand mixer fitted with the whisk attachment (or a hand mixer), beat the cream on high heat until stiff peaks form.
In a large bowl, fold together the sweetened condensed milk, whipped cream, and vanilla until smooth.
Assembly
Fold the peach puree into the ice cream base (and fresh chopped peaches if you want an extra taste of peach).
Freeze the ice cream at least 12 hours before serving.