Using a food processor or high-powered blender, puree the raspberries and coconut milk. Strain in a fine-mesh sieve to separate the seed bits from the raspberry puree. Stir and press down the mixture with a flat spoon or spatula to get as much of the puree into the bowl below as possible. Discard the solids.
Add the maple syrup, vanilla extract, and lime juice to the puree. Refrigerate for at least an hour.
If you’re using an ice cream maker, churn according to the manufacturer’s instructions for sorbet. In my KitchenAid attachment, I churn this for about 10 minutes. If you don't have an ice cream maker, you can skip the churning.
Either way, place the sorbet in a wide, shallow container until frozen (at least 2 hours). If it becomes too solid, let it soften in the fridge for a bit before serving.