Place the Coconut Milk (1 can), Avocado (2), Maple Syrup (1 cup), Lime (5), and Water (1/4 cup) into a blender or food processor and blend until smooth. For either appliance, scrape down the sides a couple of times for a smooth texture.
Pour mixture into an ice cream maker and freeze according to your machine’s instructions. The ice cream is finished when you can scoop some out, and it stays on the spoon without sliding off right away, about 20 minutes.
Serve immediately or freeze for a firmer texture. This ice cream becomes quite hard when it’s fully frozen, so it’s best to let it soften on the counter for 15 minutes or so before serving it.