Trim the very bottom of a chilled 5-pound mini seedless watermelon to make a flat base. Slice an inch or two off the top, then scoop the flesh into a blender. Puree, then strain through a fine-mesh sieve. Combine 2 1/2 cups of the watermelon juice, 1 chilled 375-ml bottle soju, 1 chilled can lemon-lime soda and 2 tablespoons lemon juice in a pitcher. Fill the hollowed-out watermelon with ice and the punch.
