1. Combine 1 1/2 cups water, sugar, and salt in a microwave-safe dish; microwave at HIGH for 3 minutes. Stir until sugar dissolves. Combine sugar syrup and cranberries in a blender; process until smooth. Strain mixture through a sieve lined with a double layer of cheesecloth over a bowl; press mixture to extract liquid. Discard solids.
2. Combine cranberry mixture, bourbon, and lemon juice in a freezer-safe bowl, stirring well. Freeze mixture overnight or until partially frozen. Scrape mixture with a fork until slushy; serve immediately.