Mix 1 cup water and 1 cup sugar in a saucepan, and heat on med-high. Once it starts to boil, turn off the heat, stir to make sure sugar is all dissolved, and and let it cool.
Juice 3 lemons, or enough to get 1 cup of lemon juice.
Put 1 cup of watermelon in a blender and puree it. Add the lemon juice and blend it up. Pour the lemon/watermelon juice and sugar water into a pitcher and fill 3/4 of the pitcher with ice and cold water. Taste, and add more water until the flavor is the right concentration for you!