Preheat oven to 350°F. Place whole peaches in a shallow baking pan and roast until very soft, about 5 minutes. Refrigerate until cool, about 1 hour. When the peaches are cool enough to handle, remove skin and coarsely chop pulp, discarding pit.

Stir water and sugar in a large saucepan over medium heat. Place the peaches pulp and accumulated juices; bring to a simmer until the sugar dissolves. Reduce heat, cover and simmer for 10 minutes.

Pour the mixture into a blender. Add lime zest and juice; and blend until smooth. Pour into a large bowl and refrigerate until cold, 4 hours or overnight.

Freeze the sorbet mixture in an ice cream maker, according to the manufacturer's directions. Serve immediately or transfer to a storage container and let harden in the freezer for 1 to 1 1/2 hours. Serve in chilled dishes.