Bring sugar and water to a boil in a small saucepan, stirring until sugar has dissolved. Remove from heat and add cilantro. Let steep 15 minutes. Pour through a fine sieve set over a bowl; discard solids. Refrigerate syrup until cold, about 15 minutes.
Puree avocados, cilantro syrup, and lime juice in a blender until smooth. Transfer mixture to a bowl and stir in milk. Cover and refrigerate until cold, at least 1 hour and up to 2 hours.
Chill a loaf pan in freezer at least 10 minutes. Freeze and churn avocado mixture in an ice cream maker according to manufacturer's directions, then transfer to pan. Cover with plastic wrap and freeze until hardened, at least 2 hours; sherbet can be frozen up to 2 weeks ahead.