Prepare an ice-water bath. Bring 1 1/2 cups water and the sugar to a boil in a small saucepan; reduce heat, and simmer, stirring occasionally, until sugar has dissolved. Remove from heat. Stir in lemon juice. Transfer to a bowl set in ice-water bath to cool. Transfer mixture to a shallow container, and freeze until just beginning to solidify, about 30 minutes to 1 hour.
Using a fork, gently scrape mixture until it is broken up and slushy. Stir in Champagne. Freeze, scraping with a fork every 30 minutes, until all of the mixture is in tiny shards, about 4 hours.
Make cassis syrup: Bring cassis and sugar to a boil in a small saucepan. (Mixture should be the consistency of runny honey; add up to 2 tablespoons water to thin, if needed.) Remove from heat; let cool completely. Strain.
Divide granita among serving glasses. Drizzle with cassis syrup.
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