One of the convicted murderers in the Epsom motel killing of 2014 has had an appeal bid knocked back.

The Supreme Court has refused leave for Leonard Gus Nattrass-Bergquist to appeal.

He and Beauen Daniel George Wallace-Loretz, both 17 at the time, were convicted of the December 2014 murder of Ihaia Gillman-Harris, 54.

The two young men were sentenced to life imprisonment in May 2016 at the High Court in Auckland.

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They claimed their attack on Gillman-Harris began because he sexually assaulted Nattrass-Bergquist and that when Wallace-Loretz inflicted the fatal blows, this was in defence of Nattrass-Bergquist.

Both defendants argued the fatal blows were in self-defence as defined in the Crimes Act.

In the Supreme Court ruling, Chief Justice Dame Sian Elias and two other judges state that Nattrass-Bergquist allegedly lied in his evidence.

"The applicant wishes to argue on appeal that a lies direction [from the trial judge] was required in this case, even though the alleged lie was in the applicant's evidence rather than in a pre-trial statement."

Section 124 (3) of the Evidence Act refers to the elements of a direction on lies: the jury must be satisfied before using the evidence that the defendant did lie; people lie for various reasons; and the jury should not necessarily conclude that, just because the defendant lied, he or she is guilty.

Nattrass-Bergquist gave evidence at the trial. Wallace-Loretz did not.

Nattrass-Bergquist's lawyer argued in the Court of Appeal that the trial judge was required to give a lies direction.

The Supreme Court said the trial judge had dealt with the fact that Nattrass-Bergquist's evidence was the only narrative relating to self-defence, but did not "give a direction dealing with the three elements referred to in section 124 (3) of the Evidence Act".

Nattrass-Bergquist's lawyer at the trial did not request that a lies warning be given. The Court of Appeal rejected the submission that an error occurred because the judge failed to give a lies direction.

At the Supreme Court, Nattrass-Bergquist's lawyer argued there was uncertainty when a lies direction should be given, when the allegation was that an offender had lied in evidence.

But Elias and her colleagues wrote: "We do not consider that the decision of the Court of Appeal creates or reflects any uncertainty about the application of section 124. Nor do we see any miscarriage arising from the way the Court of Appeal dealt with the issue."