There is no need to use "leaf" lard for soap. Unlike pie crusts, soap does not care if the fat came from under the skin or from around the kidneys. So, commercial lard (Armour, Snow Cap, etc) is fine for soap. It does have BHT and BHA added as a preservative, which you would need to research the safety of for your allergies.
As to the tests you had 15 years ago, there have been lots of improvements and changes in allergy testing since then. They also have tremendously better methods to de-sensitize than they did long ago. So, it might be worth your while to find a new doctor that has the new information. A coconut allergy is life changing, as you well know.
Yeah, I understand that, that was just me being didactic. It's terminology. Sort of like peope objecting to a soap that isn't 100% olive oil being called "castile", and other people objecting even to a 100% olive oil soap being called "castile" if it doesn't conform to a specific process. I'm a baker. I've got terminology too, LOL!