Combine peaches, lime juice, and sugar in a food processor or blender and purée until very smooth with no large chunks. You should have about 1 quart of purée. Pour through a fine-mesh strainer into an airtight container and add salt to taste. Press a piece of plastic wrap against surface of purée and chill for 2 to 3 hours, or until very cold.
Churn in an ice cream maker according to manufacturer's instructions. Transfer to a container and chill in freezer for 2 to 3 hours, or until firm.
