Remove as many seeds as you can from the watermelon (see watermelon.org for the best way to seed a watermelon). Put watermelon and water in blender and blend until smooth. Pour blended mixture, through a fine-sieve, into a pitcher, getting out all the juice, and leaving any pulp and missed seeds behind.
Add lemon juice and sugar, and stir until dissolved. Put pitcher in refrigerator and serve chilled over ice.