I'd heard of the Lazarus tale, just not the parable. The problem is that to me these are untrustworthy accounts. Even the accounts of the resurrection differ. In any case, other religions can offer the same "miracles," so Christianity is not special in this case.
Send the book, but it must make a logical case within itself without appeal to the absolute authority of the Bible (I believe it to be highly embellished history).
And, to answer your question, the author does not rely on the Bible for its own "proof".