Combine chopped mint, ginger, and honey in medium bowl. Add boiling water. Let steep 30 minutes. Strain into 4-cup glass measuring cup, pressing on solids to extract liquid. Add lemon juice and enough cold water to measure 4 cups total. (Can be prepared 1 day ahead. Cover and refrigerate.)
Fill glasses with ice cubes. Add lemonade. Garnish with mint leaves and lemon slices and serve.