In a blender or food processor, combine avocado, sugar, water, lime zest, and 2 tablespoons lime juice. Blend until very smooth, about 30 seconds. Transfer to an airtight container and stir in remaining lime juice and salt to taste in small increments. Ice cream base should have a subtle lime flavor but should taste mainly like avocado.
Cover mixture and chill in refrigerator until it is very cold (at least 45°F or 7ºC, about 4 hours), then churn in ice cream maker according to manufacturer's instructions. Transfer to an airtight container and chill in freezer until ice cream is firm enough to scoop, about 5 hours. Let sit at room temperature for 10 to 15 minutes before serving.
