Hey! I have been doing that with Lugol's and whatever oil I have been using for oil pulling. Definitely with coconut oil and it seems to "work" fine -- I use it for face-cleaning and moisturizing at night. I've also used Lugol's and red palm oil, which tastes so horrible it MUST be good for you. I may just mix Lugol's in the jar because I don't think I'll be eating it.
Another Lugol's in the Bathroom use: I made a mix of water and Lugol's in a jar for toothbrush storage. (I used to use mouthwash back in the day...). Anyway, it keeps them very clean...I do change it pretty often.