iodine is out in about 24 hours. it takes silver about a week to exit.
i would not mix the two to any great extent. one drop of Lugols in your juice in the morning is not going to hurt, but i would save the playing with bigger amounts of Iodine for when you have gone a week without silver.
i do not know of a problem for sure, but i have been erring on the side of caution on this one. i just have a feeling about it.