In a medium saucepan over high heat, combine the sugar and 6 cups of water. Bring to a boil. Cook until all the sugar dissolves. Remove from heat, add the espresso, mix, and let steep for 10 minutes. Strain the liquid into a shallow pan (about 2 inches high). Add the lemon juice and zest.
Place the pan in the freezer. Using a fork, crush the mixture every 30 minutes until it is firm but not frozen hard (should be slightly slushy), about 2 hours. To serve, spoon the slush into glasses or bowls. Drizzle with cream and garnish with more zest if desired.