The permethrin should work rather quickly. That is a heavy infestation. Poor thing should hopefully feel better. Do you see any of the lice eggs at the base of the feathers on her or the others?
Here is a video. It was difficult to handle the phone and her so I apologize for the quality.Yes, that is lice. The eggs are seen in the last photo. There is another very good product called Elector PSP that is really good and goes a long way, but is rather pricey. Here is some info about it:
Learn about Elector PSP Premise Insect Control Agent for animal usage including: active ingredients, directions for use, precautions, and storage information.www.drugs.com