Cut melon into chunks and discard rind. Purée chunks in batches in a food processor. Pour mixture through a strainer into a bowl. Pour 4 cups into another bowl; whisk in lemon juice. Save any remaining watermelon juice for another use. Pour juice mixture into 4 ice cube trays* and freeze until firm, at least 3 hours or overnight.
Make drinks: Whirl half the watermelon cubes in a food processor until broken up, then add 1 cup tequila and whirl until blended. Pour into a pitcher and repeat with remaining ingredients.
*A standard ice cube tray has 14 cube slots.
Note: Nutritional analysis is per drink.