Isn't Lain some high level multiversal by the end of the series?
Well, if Lain can rewrite the Earth, then she should win. Ciel claims Arc as Archetype Earth can do things like melt the ice of the poles, shift continents and disrupt the Earth's axis. But the best thing she has done is summon the world from 1000 years into the future and stop the Earth's rotation, both of which don't really do much here. The only chance I think Arc might have is to use her Golden Eyes to try and erase her memories, but that's only if she has knowledge of her opponent's abilities.