This is a really hard issue. I've had eczema since high school (for about 5 years). It's on my legs and chest, and not face, but I have very sensitive skin on my face too. I tried for years to use all sorts of anti-itch creams, natural and not natural, all sorts of lotions, and all sorts of soaps. Sadly, my conclusion has had to be a non-vegan steroid cream like your friends, because nothing else would help me. I don't know how bad his is, but mine gets so unbelievably unbearable (way worse then the worst poison ivy or mosquito bite), and I just had to sacrifice my morals against animal testing to help myself... Unfortunately this is often a reality to a lot of serious medical issues in our day and age because science isn't making vegan alternatives yet.
What I can suggest, however, are some things that can help reduce the symptoms a little. Because eczema is related to dryness, the key is to keep yourself as moisturized as possible at all times. It is especialy important to make sure you put a lot of moisturizer on right after showers, because that is when we lose the most moisture. So, my suggestion would be, although not very fun, to try out as many different senstive skin soaps (ideally with little to no fragrance or drying properties like glycerin), and lotions (with low water content, and high moisture content and little to no fragrance) until he finds one that helps reduce the symptoms.
Other things to keep in mind are that eczema symptoms tend to be triggered by stress, so reducing stress is important. I think because it is his face that is being effected, keeping good sun protection is key as well, because heat tends to also make it flare up.
Hope this helps, and I hope he finds a good solution.
