Combine lemon juice with 250 ml (approximately 1 cup) of water, mint and sugar, bring to a boil and remove from heat. Let rest for 15 minutes.
Remove mint and add lemon liqueur. Pour syrup into a shallow metal dish and freeze for about 5 hours. Stir every 30 minutes with a fork.
Stir finished granita thoroughly, place into glasses and garnish with lemon wedges and mint. Serve.