It was Charles Coindet, a Swiss physician, who first used iodine in the treatment of goiter.1 "Up to the present burnt sponge (l'éponge calcinée) has been the basis of all the remedies which have had any success against goiter. Arnold of Villanova [13th century] made this known.... What then is the substance in the sponge which works so specifically against goiter? It seemed probable to me that it was iodine: I was confirmed in this opinion when I learned that Mr. Fife of Edinburgh had found iodine in sponges towards the end of 1819 [*]; within six months I have already verified its surprising effects in this malady." Working with Lugol in Paris2 Coindet introduced hydriodic acid and potassium and sodium iodide. He found that certain solutions of potassium iodide were capable of dissolving more iodine (Lugol's solution) which he felt "augmented the potency of the remedy."
BLOOMFIELD AL. The History of the Use of Iodine in Toxic Diffuse Goiter (Graves' Disease). AMA Arch Intern Med. 1957;100(4):678–683. doi:10.1001/archinte.1957.00260100162020