Cut fresh watermelon into cubes, removing any seeds.
Spread the cubes in a single layer on a baking sheet and freeze until solid (at least 4 hours or overnight).
Add the frozen watermelon, lime juice, and 2 tablespoons of milk or coconut milk to a high-powered blender or food processor.
Blend until smooth, stopping to scrape down the sides as needed. Add more milk, 1 tablespoon at a time, just until the mixture comes together and has a creamy, sorbet-like texture.
Enjoy immediately for a soft-serve consistency.
For a firmer sorbet, transfer to a container and freeze for 1–2 hours before scooping.