I am sorry to say you are barking up the wrong tree with your treatment of lice.
Horses get lice (along with rain rot, goopy runny eyes, flakey dry skin, poor hair coats and many more things) from being deficient in Vitamin A.
They are NOT contagious and you cannot give rain rot or lice to a horse with healthy skin and a healthy immune system that has sufficient Vitamin A either stored or in their diet.
This is why you see lice and rain rot in thin, poorly cared for horses and in the late summer and spring on horses that are fat, but are not receiving any Vitamin A supplementation of any kind. Vitamin A is a 'fat soluble' vitamin (along with D and E) that is stored in the liver. If horses have access to good green grass they are never deficient in it. They store quite a bit if it in the fall, but if they are not supplemented, they run out of stored Vitamin A sometime in the winter. That is why we see rain rot and lice at that time in unsupplemented horses. You can see it any time of year in thin, poorly fed and cared for horses like the rescue you talk about.
You do not need to even treat rain rot or lice if you don't want to. Just get the horse on plenty of Vitamin A and it all goes away very quickly -- much more quickly than the horse that is treated with topicals and not supplemented with Vitamin A or good grass. [If you get the horse on good green grass, it will go away even more quickly.]
To treat them with Vitamin A, you can give them ORALLY the Vitamin A injectable available at feed store and vet supply stores and catalogs. It is labeled for cattle, but just squirt 5 CCs in the horse's mouth (like a dewormer) and they absorb most of it. You can repeat every week. Then, you can start the horse on a good Vitamin Supplement that has a high level of Vitamin A in it.
If you supplement Vitamin A in the winter, especially, you will never see another case of rain rot or lice, no matter how bad the weather gets.