Peel the peaches, halve and rough chop. Place them in a food processor and pulse a few times until the mixture is a coarse purée. Place the peaches in a bowl, sprinkle with lemon juice and ¼ cup sugar. Let sit at room temperature for one half-hour.
In another bowl, dissolve remaining ¾ cup sugar in the cream. Add a pinch of salt and pour the cream over the peaches, stirring to combine. Let this mixture sit in the refrigerator for a minimum of two hours and up to a day before freezing it in an ice cream maker. Follow manufacturer's instructions for freezing the ice cream.