In a medium bowl combine the yogurt, sugar, lemon juice, vanilla, and salt. Whisk until smooth.
Freeze the yogurt mixture in a 1 1/2- to 2-quart ice cream maker according to the manufacturer's directions. Stir in mint. Transfer to an airtight container and freeze for 2 to 4 hours before serving. Let stand at room temperature for 5 to 15 minutes before serving.