Line a rimmed baking sheet with parchment paper or a silicone baking mat. If using a whole seedless watermelon, cut it into quarters. Working with one quarter at a time, make parallel cuts about 1 inch apart into the flesh, stopping at the rind. Rotate the watermelon quarter 90 degrees and repeat to create a crosshatch pattern. Cut between the rind and the flesh to remove the flesh, then slice it crosswise into 1-inch cubes. Arrange the cubes in a single layer on the baking sheet and freeze until solid, at least 3 hours or overnight.

In a blender, combine 2 ½ cups of the frozen watermelon cubes, ½ cup of frozen strawberries, 1 cup of light coconut milk, ½ cup of plain Greek yogurt, 1 tablespoon of honey, and 1 ½ teaspoons of lime juice, if desired. Blend, stirring as needed, until smooth and creamy, about 1 minute. Pour the mixture into 2 glasses. (Any leftover frozen watermelon cubes can be transferred to freezer zip-top bags and stored for up to 2 months.)