Lawyer Mark McDonald said he was seeking permission from the Court of Appeal to take the "exceptional, but necessary, decision" to apply to reopen her case.
He claimed key medical expert Dr Dewi Evans had changed his mind over the mechanism of death involving three of Letby's victims.
Letby, 34, is serving 15 whole-life orders for murdering seven infants and attempting to murder seven others, with two attempts on one of her victims, between June 2015 and June 2016.
Following two trials at Manchester Crown Court, Letby also lost two bids to challenge her convictions at the Court of Appeal - in May and most recently in October.
Findings
Mr McDonald said: "The primary grounds of appeal at the previous hearings related to the admissibility before the jury of the evidence of the lead prosecution expert Dr Dewi Evans.
This story is from the {{IssueName}} edition of {{MagazineName}}.
Start your 7-day Magzter GOLD free trial to access thousands of curated premium stories, and 9,000+ magazines and newspapers.
Already a subscriber ? Sign In
This story is from the {{IssueName}} edition of {{MagazineName}}.
Start your 7-day Magzter GOLD free trial to access thousands of curated premium stories, and 9,000+ magazines and newspapers.
Already a subscriber? Sign In
Eddie has know-Howe to keep Isak at Toon
EDDIE HOWE is targeting a Champions League return as he bids to fend off interest in Newcastle's star striker Alexander Isak.
WE'RE ALL IN IT TOGETHER
Unhappy Martinez urges the United players to put some pride back in shirt
Hunt on for one more Mo record
GOALS CHASE MAY YET INSPIRE SALAH TO STAY
JACK UNFAZED BY NEW STATUS
Draper won't lose sleep over filling Murray's big shoes
Bunting is hoping better sleep can also revive Smith
STEPHEN BUNTING says hypnotism saved his career - and now Michael Smith could be heading for the last trance saloon.
IAG shares soar as BA plans £7bn business transformation
ANALYSTS are backing IAG shares next year as the group’s flagship British Airways brand pushes ahead with a £7bn transformation plan.
Veteran survived D-Day to become UK's oldest man
Desert Rat sniper Donald is 110 today
Hero saved lives in Hamas attack unaware his son had been killed
A HERO ambulance volunteer who helped save dozens of wounded victims in the October 7 Hamas attack was unaware his son had been murdered in the assault.
Dementia expert's Christmas advice for family gatherings
A LIFESTYLE expert has compiled a guide for Daily Express readers on how to approach the subject of dementia with children at Christmas.
Keir pledge to Kyiv on training troops
SIR Keir Starmer yesterday spoke to Ukraine's President Volodymyr Zelensky, with the pair agreeing to \"refine\" UK training of Kyiv's armed forces.