Puree the watermelon in batches, using a food processor or blender.

Pour the puree into a mesh strainer to separate the liquid from the pulp.

Save the pulp, and if desired, reserve the juice for another use.

In a large mixing bowl, add sweetener to taste (if your melon is very sweet, you may need less), along with lime juice and zest. You will have approximately 6 cups of watermelon pulp.

Mix well, and pour contents into the frozen bowl of an ice cream maker.

Churn for about 30 minutes, and serve.

If you don't have an ice cream maker, pour the contents into an 8 x 8 metal baking pan and freeze for about 1 hour. Remove from the freezer and break up any frozen parts with a fork. Cover with foil, and return the pan to the freezer for about 1 ½ more hours.

Store any leftovers in a covered container in the freezer. Before serving, let sit out for 20 minutes or microwave for 20-30 seconds so ice is easier to break apart and serve.