One solution might be to use any case and a strip light like the one linked to below. I bought one of those a couple years ago for one of my neighbors. It wasn't this particular one but one pretty much like it. It worked really well. She uses a Kindle 4 and it fits nicely between the case and the Kindle and bends down into a nice position for reading. I'm not sure how long the batteries last.
https://www.amazon.com/Freedi-Flexib...ds=ebook+light
Barry