Puree watermelon in food processor in batches. Measure out 4 cups puree and place in bowl. Add sugar syrup and lemon juice. Stir to combine. Freeze in ice cream maker according to manufacturer's instructions.
(Simple Syrup: 1 cup sugar to 2 cups water, bring to boil over, reduce heat and simmer until sugar dissolves and mixture is clear. 2 1/2 cups).