Combine sugar, water, and mint leaves in a small pot over medium heat; cook until sugar dissolves and mixture is thick and syrupy. Remove from heat. Strain out mint leaves and discard. Cool syrup to room temperature, about 20 minutes.
Combine brewed tea with lemon juice in a bowl with a lid. Stir in syrup. Refrigerate until temperature reaches 40 degrees F (4 degrees C), about 20 minutes.
Pour tea mixture into an ice cream maker and freeze according to manufacturer's instructions for sorbet, 10 to 15 minutes.