Bamber has probably convinced himself he is innocent. Or at the least justified in his actions due to the hatred and raw deal he believed he was getting. He told Julie why each person should be killed.
The lie detector test was no preasure. The questions would be expected. He would just have to say 'yes' or 'no'. A failure would not be reported by the CT. Someone as calculated as Bamber was always likely to pass. Which is why he kept requesting one.
If - for the sake of argument - we assume for a moment that polygraph tests are valid and can be relied on, the reason Jeremy was able to pass is that he has constructed an alternate narrative of the case that he has come to believe, because he has to, either because it is true, or because he is guilty and needs to believe in this alternate narrative. In the latter case, the alternate narrative could be a projection of his own guilty conscience.
All liars, petty and serious, engage in a form of double-think in which they know what they say is not true but they also believe in it. That may sound odd, but if you think about it, it makes sense. If you've done something wrong, you may easily come to convince yourself that you didn't do it. Liars on this scale often come to sincerely believe in a completely alternative world and in effect become schizoid and delusional.
Of course, that's just speculation in the case of Jeremy. In any event, polygraphology is too simple. It does not take account of psychological nuances. It is easy to imagine an innocent person failing a polygraph because innocent people are, by the very nature of their innocence, doubtful about facts and may be nervous and so on. Equally, a guilty person is nervous, but knows what he has done and this knowledge may give him the confidence to ride through a fine-tuned test of his physiological responses. Or it may not. We're left in the same place with the same questions. A polygraph result is practically useless.
