Hey there!
When it comes to eczema the most important thing is to keep the skin from drying.
Do you make your own soap? I'd suggest finding or making something as mild as possible (some 100% olive oil soap, often called castile, with a generous superfat of around 8%, unscented).
I'm sure that if you don't make soap yourself someone on this forum will be happy to send you some.
I'd use that soap once a week only; and for the other bathing/showering times I'd use an oil.
You could use part emu oil, part olive oil and add 1% of essential oils. 2 parts lavender, 2 parts tea tree and 1 part sandelwood would be a good combination.
Just put it in a bottle and shake well before use. Don't use any soap or detergent on her during the bath/shower (always short and not too warm, that dries the skin out too) and rub the oil on her while she's still wet. Dry her off afterwards.
Also, I wouldn't make a lotion (beacause lotions always need a preservative, and this could make her problems worse) but rather make a balm or solid lotion.
There's plenty of info on those 2 here; but if your questions aren't answered, you can always open a topic about those products
Good luck,
Dagmar