As an inquiry into his death opened on Tuesday, the Bayoh family solicitor, Aamer Anwar, challenged the police officers involved to give a full testimony if they had nothing to hide.
The public inquiry, chaired by Lord Bracadale, is set to examine the circumstances leading up to the incident, and the following management process and investigation into the death.
It will also look to establish the role the father-of-two's race may have played in his death.
Mr Anwar said the inquiry would have never happened had it had not been for the "courage and perseverance of Sheku's loved ones who have refused to walk away, be silenced, bullied or patronised".
"Over the years, it has become clear to the family that the police, Pirc (the Police Investigations and Review Commissioner), and Crown Office, has operated an unholy trinity of dishonesty, racism and incompetence, betraying the word justice," he told a press conference.
"Kadi Johnson (Mr Bayoh's sister) has no doubt that the way Sheku or her family were treated by the justice system would not have happened had Sheku been white, their treatment was compounded by repeated attacks from those who remain in a child-like denial about the existence of racism in policing today.
"Kadi has described Skeku as Scotland's George Floyd, but taking the knee and Black Lives Matter will mean nothing if Scotland fails to support justice for Sheku."
Mr Anwar added: "In less than 50 seconds of the first police officers arriving, Sheku Bayoh was brought to the ground, he was handcuffed and retrained with leg and ankle cuffs, and would never get up again, losing consciousness and dying.
"As Kadi said when they put her brother's lifeless body in the ambulance, he was still shackled like a slave, with over 24 separate injuries, cuts, lacerations, bruises and a broken rib.
"Within minutes, the process of criminalising, smearing and stereotyping began to enforce an image of a mad and dangerous black man, wielding a knife and with stereotypical characteristics of extraordinary strength in an attempt to blame Sheku for his own death, but he was unarmed and never deserved to die."
No charges have been brought because of his death, but Mr Anwar said the family felt if the police officers involved had nothing to hide they had "nothing to fear from coming and giving a full and frank testimony to the inquiry".
He said the "real test of this inquiry" would be "whether this country acts to ensure that real change takes place in an unaccountable, all powerful justice system".
"Sadly, Sheku is not by any means to first man to die in police custody but, if anything, I hope that his name does not fade from memory and that one day the name of Sheku leaves us a legacy that his children can be proud of," he said.