There is no scriptural support to say a lost man cannot believe. He cannot break free of his bonds to sin. But he is still able to believe or not believe.If you truly turn to Him, you have already been set free. The fallen, lost, dead man can not, and will not do this, seeing he is unable to do so.
I'm not sure how Lazurus, a depiction of the Resurrection, has to do with what we are talking about.It would be like the Christ seeing Lazarus coming out of the tomb and then making him alive.