Combine the peaches, ½ cup of the sugar and the lemon juice in a medium bowl. Stir well, cover and refrigerate overnight.
Warm the milk, remaining ¼ cup sugar, 1 cup of the heavy cream and the salt in a medium saucepan over low heat, stirring until the sugar is dissolved.
Pour the remaining 1 cup heavy cream into a large bowl and place a fine-mesh sieve on top. Whisk the egg yolks in a medium bowl. Slowly pour the warmed milk mixture into the egg yolks, whisking constantly. Scrape the mixture back into the saucepan.
Place the saucepan over medium heat and stir constantly with a rubber spatula, being sure to scrape the bottom of the pan as you stir, until the mixture thickens and coats the back of the spatula, a few minutes. The mixture should register 170 to 175 degrees F on an instant-read digital thermometer.
Pour the custard through the fine-mesh sieve and stir it into the cream. Stir in the vanilla extract and place the bowl over an ice bath. Stir occasionally, until the mixture is cool. Cover and transfer the custard to the refrigerator until completely chilled, at least 8 hours or overnight.
When ready to churn the ice cream, place a fine-mesh sieve over the bowl with the custard and pour the peaches into the sieve, allowing the accumulated juice to strain into the custard. Whisk the juice into the custard and set the peaches aside. Freeze the mixture in your ice cream maker according to the manufacturer's instructions, adding the peaches when the churning is about three-quarters complete. Transfer to a freezer-safe container and store in the freezer.