Whisk first 5 ingredients in a 2-quart pitcher or large bowl until blended. Cover and chill 30 minutes.
Pour milk mixture into freezer container of a 1-quart electric ice-cream maker, and freeze according to manufacturer’s instructions. (Instructions and times will vary.
Remove container with ice cream from ice-cream maker, and place in freezer 15 minutes. Stir together figs, lemon juice, sugar, and chopped fresh mint. Stir mixture into prepared ice-cream mixture. Transfer to an airtight container; freeze until firm, about 1 to 1 1/2 hours.