My derm confirmed to me that yes, there are sebaceous glands in the lips.
We also noticed seb derm in my mustache and the recommendation was to keep clean shaven.
I highly doubt anyone has done this strict diet for that length of time. Lees success could have also been from eliminating an allergy in the process. I think if you go to the trouble to do the diet you should do an Elimination Diet as well, gradually re-introduce first veggies, then fruits, then your meats and nuts.