i didnt get the brown pee until my fourth month on at least(almost always more) 16 drops of Lugols or 100mg+ of iodine.
two things did change about that time which may have effected it. i got some iodoral and started taking it, 2-4 tabs, in addition to my lugols. i also made my own Lugols and put an extra gram of I2 per 100ml in it. frankly, i think the added elemental Iodine helped. also, i think my first 500ml of Lugols was old or irradiated or something. this new stuff i made myself is much better. iodoral is more effective than lugols, i think.