Matthew Johnson was jailed for life in 2011 for the bludgeoning murder of Williams in a high security unit of Barwon Prison, near Geelong, in April 2010.
He used the stem of an exercise bike seat to fatally bash Williams, who had just returned to the unit after a visit from his father George Williams.
Johnson is a decade into the 32-year minimum sentence he was handed for the slaying, but has filed an appeal against his conviction. He is being represented by barrister Jason Gullaci.
No details of the appeal grounds were given during a hearing in the Victorian Court of Appeal on Wednesday morning, but Mr Gullaci revealed a link to Victoria's Lawyer X scandal through references to the royal commission and an earlier Ombudsman report.
Johnson appeared by videolink from prison, while Mr Gullaci also joined the hearing remotely.
He fired up during submissions to Judicial Registrar Deirdre McCann about difficulty accessing documents from Victoria Police and Corrections Victoria.
Mr Gullaci said a lot of the information sought was based on sworn evidence given by Victoria Police officers, or statements made by them.
"We'll leave to one side whether people think we're going on a massive fishing expedition or whether we've got a legitimate forensic purpose, but we say there is a real basis based on sworn evidence given at the royal commission for the claims for documents that we're seeking," he said.
He also called on Corrections Victoria to "stop playing games".
Johnson's legal team has requested, among other things, a photograph from Corrections Victoria.
However, they were told the photo couldn't be sent unless Johnson's lawyers gave it to the department first.
"Well that's a bit difficult seeming we're asking Corrections for the photograph," he said.
Johnson has until February 4 to put forward submissions in his appeal, with a response due from Victoria Police Chief Commissioner Shane Patton on February 18.
A further directions hearing in the matter will be held on February 24.
Johnson maintains his innocence in Williams' murder.
At trial he argued he acted in self-defence, something Justice Lex Lasry described in sentencing Johnson as "fanciful".
He instead found Johnson killed Williams because he knew the underworld killer - who was serving multiple murder sentences - was providing information to Victoria Police about the murders of police informer Terence Hodson and his wife Christine in 2004.
Johnson was a leader of the Prisoners of War, a gang with a hatred of anyone who cooperates with police.
Williams had provided multiple statements to police implicating himself, former policeman Paul Dale and hitman Rodney Collins in the Hodson murders.
Mr Dale and Collins were both charged with the murders when Williams was killed, but charges were dropped just weeks later.
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