Dickey was aged 16 at the time of the murder and Brown was aged 19.
While neither Dickey nor Brown stabbed Mr McAllister, they were a party to the murder taking place.
Katrina Roma Epiha is also appealing her sentence for the murder of Alicia Nathan who she stabbed to death at Avonhead in Christchurch on August 5, 2017 over an argument about loud music.
Epiha, who plead guilty to the charge, was 18 at the time she murdered mother-of-one Ms Nathan.
The matter is being heard in the Court of Appeal at Wellington by Justices France, Miller and Collins.
Counsel say the sentences were manifestly unjust and disproportionately severe when taking into account their age at the time of offending and the scientific proof regarding brain development of young people.
That being the case, their culpability for what they did, was diminished.
The three appellants are seeking to have their life sentences quashed and finite sentences imposed which will also mean they will be not subject to recall for the rest of their lives if they were to offend again in the future.
Yesterday Brown’s lawyer Lisa Preston said while the New Zealand court had recognised features of adolescent development with regards to offending, there was now far greater research done on brain function between adults and young people including cognitive decision making.
"As in Mr Brown’s case a deeply absolutely wrong response on every level by the group and by the members of the group to what they perceived as an outrageous situation and which they responded to in a way that is absolutely mirroring the sort of factors that accompany these deficits in the brain as the science shows."
It was her submission that the weight to be afforded to youth and the reasons under-pining it in regard to manifest injustice, was not sufficiently recognised at sentencing.
Also appearing for Brown, Fiona Guy Kidd, QC, said his co-offender Laura Scheepers, who was involved with the luring of Mr McAllister to the stadium and then telling the group when it was an appropriate time to come, was found guilty of manslaughter and had received a sentence of home detention.
"That shows quite starkly that I would suggest manifest injustice for one who will have a life sentence, with that ability for her to rehabilitate and move on with her life."
Brown had suffered from abuse, neglect, trauma and had been been placed in 57 foster homes as a child.
"As the Royal Commission found he is an example of their findings that abuse has a profound impact on relationships survivors need to navigate in their everyday lives."
Dickey’s lawyer Fergus More said his client was highly remorseful for her actions.
Her motivation was that she says she was sexually assaulted by Mr McAllister, yet knows if she had not disclosed that information to her friends, he may still be alive today.
"She was driven to an outcome that ultimately ended in his death."
Epiha’s lawyer Hunter de Groot said his client had been diagnosed with PTSD and was a person who had been raised in an environment where threats needed to be taken seriously and where extreme violence was modelled as a solution to problems.
He asked the rhetorical question of whether she would have reacted the same had she not had the PTSD diagnosis or been exposed to that environment growing up.
"In a real sense that can never be known, I accept that, but certainly you have to think that these factors in her background were very high risk for this completely maladaptive response in the situation she found herself in."
The hearing continues today.
