Weird and interesting question! Would lotion/ hair oil or any other cosmetic be detrimental during an extended dry fast?
Might be an unpopular opinion, but most lotions and hair oils are probably detrimental, in general. Unless you’re rubbing tallow or coconut oil or something on yourself.
Your skin is a semi-permeable organ and will ‘eat’/absorb many things that you put on it.
I would tend to say to abstain from as much as you can while DF’ing, but the Phoenix Protocol guy spends a decent amount of his DF days in a little cold water tub in his yard, so each individual has to make some judgement calls on where they, personally, draw the line for their particular health journey.