safe to eat eggs when treating for lice?

I have read through a bunch of old threads and have plenty of ideas now on how to treat for lice.
DE, VCO, Poultry Protector, permethrin, etc.

what I haven't been able to find is a consensus on a) if I need to not eat eggs for a while, and b) if so, how long?

I just found out tonight that we have a lice problem. My dd's little pet runty rooster is absolutely infested... I feel like the worst chicken keeper ever, He has always been "special" but has been acting a bit more off and then she came in and told me she thought he had pastey butt. I was surprised since he was born on Easter and is certainly too old to have pastey butt, but I checked and there are literally ROCKS hanging off of him. I did a little google and see that he is simply covered in lice .

I plan to check the rest of the flock tomorrow and see how bad it is. he is kind of a loner, but does sleep in the same coop, so I'm sure it's an issue.

I want to do a major knockdown so I guess I'll use the permethrin and dip them, but then how long to not use eggs? Or, if I see that on the rest of the flock it is minor, can I just spray them with the poultry protector and keep eating eggs? I know that we have to thoroughly clean the chicken house (how fun ) nesting boxes, etc.