Hi there
Don't know the answer as I don't feed Lily's kitchen, but can't say I have had problems with fish skins - altho a different brand, I imagine they are all made in much the same way, and there is not much to them - so wouldn't have thought they would affect
his appetite to that extent.
Have you made sure he is ok health wise, if he is lethargic it may be worth checking there is nothing going on.
Sorry I can't be more help - hopefully someone who has experience of feeding Lily's Kitchen will have some guidance.
Hope it sorts itself out ASAP