My son had dreadful eczema when he was younger. It would weep all night while he was sleeping, and in the morning when he woke his little sleep-suit would be stuck to him. Torso, legs, arms, face... poor little guy. I asked the doctor if it was anything I was eating ( he was solely breastfed at the time, aged 4 months) and she said no, don't be silly and here's some steroid cream to put on your baby's skin...
Don't use soap everyone said, just put a bit of oil in the bath water, try sweet almond oil because it's good for skin...
Fast forward two months and I was back in NZ on holiday and went to see an alternative health practitioner here. Turns out he was allergic to dairy, eggs and nuts and once I stopped eating those ( yes it was VERY MUCH caused by what he was getting from my food via breastmilk) his eczema cleared up virtually within a week! And I stopped using the almond oil in the bath - being that he was allergic to nuts!
Anyway, after getting all that off my chest, he is now 12 and still allergic to eggs and nuts, but can tolerate dairy ( although he doesn't eat much of it because he doesn't like it, unless it's ice cream, lol) and he can use anything on his skin now and it's fine.
Having said that, my sister in law, and my friend's daughter who have eczema ( the latter far more severely) have both stated that my homemade soap is a non-irritant for them. There's nothing special about my recipe, and I'm sure that you will find if she is using commercial soap, that, by comparison, your homemade soap will seem far more gentle. Just keep the CO down to below 20% and consider having a slightly higher superfat. Make sure that any of the oils you use are non-irritants for her. Some people can't tolerate OO for example, even though most say it is very mild. Don't bother with fancy additions like neem oil or other expensive oils because that kind of expense is better put into leave on products. Although, I do add aloe juice (homemade) oat milk ( homemade) and coconut milk to some of my soaps and they are lovely additions that are not expensive. To start, I wouldn't bother with any of those, just make a good base recipe and see if she can tolerate it first before making additions or tweaks.
Good luck!