Add the frozen watermelon, honeydew, or cantaloupe to the bowl of a food processor with the sweetener, lemon juice, and water or non-dairy milk. The amount will depend on the power of your machine but start with less (around 1/2 cup), and add more as needed. For the honeydew, I ended up using about 1 cup. Blend until smooth, scraping down the sides periodically. It will take some time to get it smooth.