Is lighting a green screen necessary?
You'd probably want to light it anyway, as it will make it easier to pull a key if it's properly lit. The farther you can keep it away from the objects or talent you'll be keying, the better. But light is essential to accurately capturing color, so if you can light it, you should. You want it to be evenly lit so that you don't have to choose too wide of a color range to key out.