To prepare the melons, cut them open and scoop out the strings and seeds and discard them. Carefully cut off the rind and discard that as well. Cut up the melon and place into a blender or food processor and purée well until smooth and soupy. Set aside in a bowl.
Make a simple syrup by placing the sugar, water, and lemon zest in a saucepan over medium-high heat. Heat until the sugar has melted and the mixture has come to boil. Remove from heat. Add the mint (if using) and let sit for 10 minutes. Strain out the lemon zest (and mint if using).
Combine the simple syrup, citrus juice, corn syrup, and salt with the puréed melon. Stir well. Cover with plastic wrap and allow to chill completely in a refrigerator. (Chill for several hours or overnight.)
Process in an ice cream machine via the manufacturer's instructions. The sorbet will have a soft texture right out of the ice cream maker. If you would like a firmer consistency, transfer the sorbet to an airtight container and place in a freezer for an hour or two. Once frozen, you may need to let it sit for a few minutes at room temperature to soften before serving.