Make sorbet syrup: In a very small saucepan over medium heat, cook sugar with 2 tbsp. water, swirling pan, until sugar dissolves, 1 1/2 minutes. Cool completely.
In a bowl, mix juices and 3 tbsp. sorbet syrup. Taste and add more syrup if needed; it should be slightly too sweet (it will taste less sweet when frozen). Chill until cold, 2 hours.
Churn in an ice cream maker until softly frozen, 15 to 20 minutes. Eat right away, or transfer to an airtight container and freeze until hard, at least 2 hours.
Make ahead: Sorbet syrup, up to 1 month, chilled airtight. Sorbet, up to 1 month, frozen (scrape with a fork to fluff before serving).