The pharmacist told me not to use it for eczema (although I think it does say on the pot that you can). She said the reason it's so effective for nappy rash is because it's drying - so the opposite of what you want with eczema. Also she said it contains lots of fragrances compared to most eczema ointments, as well as lanolin, and that eczema sufferers are more likely to be irritated by wool (and therefore by lanolin) than people without eczema.
As an aside, I have mild eczema, and find wool clothing brings me out in hives, but it took me aaages to figure out why lansinoh was making breastfeeding more painful instead of less when I first had DS 🙄 So, anecdotally, I can believe that lanolin-containing products might not be great for people with eczema.