Even in the organic system you can use crovect (which is hideous in so many respects) to treat fly strike - the sheeps welfare has to come first. How do organic peeps deal with lice? scab?
I don't know because like you said, in the organic system they allow some quite harmful things... I favor natural methods, and am very much a learner in that area, but in general the way to treat lice as well as all other internal and external parasites seems to be best done through diet, and sometimes topical application of stuff such as garlic, wormwood, etc.
My merino ewe got to be as big as a table despite being a bottle-fed orphan, and she ate an entire wormwood bush that was bigger than she was. In the course of a week or so she killed it, eating well and truly beyond the supposedly lethal amount. She was never mulesed, crutched, treated with anything for worms or lice, but never had any problems with any parasites whatsoever, and never even got a dirty fleece. You could spot her from miles away, gleaming and enormous compared to the herd.
With my poultry, I just use raw garlic, never treat them for worms beyond occasional 'boosts' of chili, never treat the coop nor birds for mites or lice, because while the bird's bodies are infused with garlic, the internal and external parasites can never take hold, and neither can most viruses and diseases. Feeding raw garlic as part of their staple diet has made me lazy, I must say, lol.