There's no easier trip from fruit to dessert than sorbet. Especially this one, which is also kind to frozen peaches, and doesn't even make you remove the skins.
Combine peaches, lime juice, and sugar in a food processor 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.