Cut a ripe, seedless watermelon into small cubes, ensuring to remove any black seeds. Line a baking sheet with parchment paper and arrange the cubes in a single layer. Freeze for at least 4 hours or overnight until completely solid.

Transfer the frozen watermelon cubes to a high-speed blender or food processor. Add 1 tablespoon of fresh lime juice. Blend until smooth, pausing to scrape down the sides as needed. If the mixture is too thick, let it sit at room temperature for 5 minutes or add 1 to 2 tablespoons of water to assist.

For a soft-serve consistency, serve the sorbet right away. For a denser texture, spoon the blended mixture into a loaf pan, smooth the top, cover, and freeze for 1 to 2 hours. Use a warm scoop to serve clean rounds.