Combine the first 3 ingredients in a medium saucepan; bring to a boil. Remove from heat; strain mixture through a double-layer cheesecloth-lined sieve into a bowl. Discard solids.
Strain lychees through a colander into a bowl, reserving 1/2 cup liquid; discard remaining liquid. Combine lychees and 1/2 cup liquid in a blender, and process until smooth. Strain mixture through a double-layer cheesecloth-lined sieve into bowl over ginger mixture. Discard lychee pulp.
Pour the lychee mixture and ginger syrup into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon the sorbet into a freezer-safe container; cover and freeze 1 hour or until firm. Serve sorbet with Fruit Salsa. Garnish with mint sprigs, if desired.