[chronotrig]

I'd add that Will wouldn't be wrong in calling them two sides of the same coin. If Lion survives, "Yasu" would never go to Rokkenjima. So the character we know as "Yasu" would never exist. That way, even if they are different people, neither can live if the other survives.

Also, if Yasu never learns that she isn't actually Lion (she keeps saying furniture until the end, so this is probably possible), then she wouldn't write that fact into the message bottles.
In other words, inside the fictional stories, Yasu might actually be Lion. And Clair seems to represent Yasu in the fictional stories, since she talks about being responsible for the murders.