Questiff I think you have to be mindful of how the lips change over time and this is best done by taking photos. You may release that the redness/inflammation is in fact always there but changes in diet like you mention are usually calorie restrictive and this can slow the immune system and the healing cycles making it appear as though it is having a positive effect when it fact it isn't.
In my blog you can visibly see how I started with a lot of inflammation (redness) as this is an area where the skin has all been stripped away, and it takes constant application of a barrier to allow it to heal.
I would not get caught up in the dietary concerns until you try the leave alone/moisture method first.