Combine the fresh raspberries and water in a blender and process until completely smooth, about 1-2 minutes. Pour the puree through a fine-mesh strainer into a bowl, pressing gently with the back of a spatula to extract all the liquid while leaving the seeds behind. I like to do this step over a bowl so I can save every drop of that beautiful raspberry juice—the seeds can make the sorbet grainy, so don't skip the straining.
Add the cane sugar, vanilla extract, lime juice, and sea salt to the strained raspberry puree. Stir vigorously for about 2-3 minutes until the sugar is completely dissolved—you should not feel any graininess when you rub the mixture between your fingers. The salt won't make the sorbet taste salty; instead, it enhances the raspberry flavor and rounds out the tartness from the lime juice.
Pour the sorbet mixture into your ice cream maker and churn according to the manufacturer's instructions, typically 20-30 minutes, until the mixture reaches a soft-serve consistency. Transfer the churned sorbet to a freezer-safe container and freeze for an additional 1-2 hours until it reaches a firm, scoopable texture. I find that scooping it directly from the ice cream maker is tempting, but those extra couple hours of freezing will give you that perfect dense, smooth sorbet texture you're after.