Both of them lied. One of them did so in court. The other did so to the police. At no time during his interrogation did Lucie invoke his right to remain silent or his right to counsel, both of which he was mirandized on. Lucie voluntarily submitted to polygraph following his arrest. He failed it. Prior to trial, both counsel agreed to the trial judge's instruction to leave the polygraph issue alone unless defense brought it up first. Defense brought it up in front of the jury, whereupon prosecution brought up the fact that Lucie had failed the polygraph. Defense objected and was overruled.
Polygraph is well known to be little better than tea leaves. Given that, maybe he will win a new trial based on incompetency of counsel.
little better => NO better