First area of consideration would be what is she allergic to? I have had eczema sine age 2 (very long ago) anywhere from mild to life threatening Severe. Yes eczema can certainly be life threatening. If she is allergic to bees please do not add in honey or beeswax. Pine Tar can be a severe allergin, so be careful with it. Shea can be very bad for people with latex allergies. Best suggestion would be to keep it simple. If not opposed to using lard, it makes a wonderful soap mixed with very light pure olive oil, some castor and 18% coconut oil. Again please weed out what causes her eczema, including eo's, or if she just has dry skin, make a very mild bar using emollient oils such as sunflower, avocado, or rice bran. Other than the avocado, the other oils should be used in the 10-15% range. Canola is also a favorite of mine.
Personally my skin loves loves salt bars and all things salt. It helps keep the itching at bay. Lavender & peppermint is a very nice eo combination for eczema. Oatmeal depends on whether oatmeal bothers her. Neem oil also works for some, but start with a small test batch of neem soap with a low percentage of neem to start. Trust me try salt bars! I even make myself a salt scrub in a cream soap base with jojoba lavender oil that has kept me off predisone for 1 yrs now. (stops the itch). Avocado oil contains a plant steroid which can also help. Flax Seed oil can also be a high allergin. Keep it simple with no exotic oils until you are sure what can be used. The same goes for any leave on products and they should always be tested in a small area, inside elbow is the best. LOL, you will see I am very passionate about "eczema". Many will say she just has eczema, well I have almost died more than once from "just eczema".