Toss the peaches with 1/2 cup sugar and lemon juice. Let sit 30 minutes to 1 hour until syrupy.
Mash the peaches until only very small pieces remain. Strain and reserve both the peach syrup and mashed peaches. Chill.
Heat the cream, milk, 1/2 cup sugar, and salt in a saucepan over medium-low heat until hot but not boiling.
Whisk the egg yolks with the remaining 1/4 cup sugar until lighter in color.
Slowly whisk 1/2 cup hot cream mixture into the yolks, then another 1/2 cup to temper.
Return the tempered yolks to the saucepan and cook, stirring, until 170-175°F and thick enough to coat a spoon.
Remove from heat and stir in the vanilla extract.
Strain the custard into a clean bowl and stir in the reserved peach syrup. Refrigerate for 4 hours until thoroughly chilled.
Churn the chilled base in an ice cream maker for 25-30 minutes.
Add the reserved mashed peaches during the last 30 seconds of churning.
Transfer to an airtight container and freeze 4-6 hours before serving.