In a bowl, whisk together yogurt, lemonade concentrate, half-and-half, lemon juice, and sugar until sugar is dissolved.
Chill until cold, about 30 minutes.
Freeze mixture in an ice cream maker (1½-qt. capacity) according to manufacturer’s instructions, until motor stops or dasher is hard to turn. Transfer to an airtight container and freeze until firm enough to scoop, about 2 hours.