Good of you to point that out. I read some instructions I found at another site 3 times before the "iodide first" sunk in. It seems that the potassium Iodide is what makes the elemental Iodine water-soluble.
"Potassium Iodide renders the elementary Iodine soluble in water through the formation of the triiodide (I3−) ion. It is not to be confused with tincture of Iodine solutions, which consist of elemental iodine, and Iodide salts dissolved in water and alcohol. Lugol's solution contains no alcohol."