Lex was not dead - though through no effort of his own. It was just that, within this specific zone that divided the inner and outer jungle, the fundamental laws of the universe did not function.
Even though Lex was an Earth immortal, and all round badass, his existence still depended on the functioning of laws - the deeper, more esoteric laws that he could not yet sense, nor influence through his tenet.
As such, the moment he entered that barrier, his body, which was dependent on those laws to exist, stopped existing. Yet he lived. That was because the nature of the soul was such it - on an absolutely fundamental level - did not rely on those specific laws to exist.
That put Lex in a state of existence that was in an unusual limbo. Instead of entering his soul state - which is how he would have entered the barrier if he had known about how it functioned - Lex was in a state of being and not being.
