Combine the sugar and water in a small saucepan over medium heat. Stir just until the sugar dissolves and the syrup is clear, 2β3 minutes. Remove from heat and cool to room temperature.
Prepare the mango by peeling, pitting, and dicing. Measure 4 cups of diced mango.
In a blender, combine the mango and lime juice. Blend until completely smooth, 30β60 seconds. Add the cooled syrup and blend briefly to incorporate.
Pour the mixture into a covered container and chill until very cold, 2β3 hours or overnight.
Stir the chilled base and churn in an ice cream maker until it reaches a soft-serve texture, 15β25 minutes, depending on the machine.
Transfer to a shallow freezer-safe container, press parchment directly onto the surface, and freeze until firm enough to scoop, 2β3 hours. Let sit at room temperature 5 minutes before scooping if needed, then serve.