I'm posting this in answer to a request. I haven't made it myself. It was on a site called The Ice Cream Parlor. An ice cream maker is necessary. Times do not include chilling or freezing, and are guesses.
- Cook the sugar, water and lemon juice together, stirring occasionally until the sugar is dissolved.
- Remove from heat and chill.
- Cut up the watermelon and remove all seeds.
- Puree in a blender or food processor.
- Stir into chilled syrup.
- Freeze in an ice-cream maker according to the manufacturer's instructions.
- Pack into an airtight container and store in the freezer.