To get rid of Lugol stains .... dampen powdered Vitamin C (ascorbic acid) and rub onto stain. This works on inanimate objects and will probably work on fingers too!
Great tip there Josie29, if you happen to have Vitamin C powder.
I was able to get similar results using white vinegar (acetic acid).
I did this as an experiment after reading your post.
Stained my finger with Lugol's, soaked a rag with vinegar and used it like a washcloth on the area. Stain gone after a couple minutes.
Decided to try this because I don't have Vitamin C powder but do have a jug of vinegar.
Is there anything vinegar can't do?