Murdoch's lawyers had sought permission to appeal against the sentence saying the trial court was wrong to allow Lees's "tainted" evidence, claiming she had seen an internet photograph of him a month before reporting him to police.
Lees's testimony was central in proving that Murdoch shot Falconio in the head after flagging down the couple's camper van near the outpost of Barrow Creek.
At the trial, she said Murdoch threatened her with a gun, punched her in the head and bound her with cable restraints.
She told the court how she managed to escape and cowered in the bushes for hours as her attacker hid Falconio's body and then stalked her with a dog.
Falconio's body was never found despite attempts by Aboriginal trackers and a clairvoyant to locate it.
The authorities believe Murdoch hid the corpse somewhere in Australia's vast interior.