Mohammed Asghar, who lived in Edinburgh until a few years ago, was arrested in 2010 in Rawalpindi, near the Pakistani capital Islamabad, for claiming to be the Prophet Muhammad. The 69-year-old has already attempted suicide in jail.
His family said he was treated for paranoid schizophrenia at Edinburgh's Royal Victoria Hospital before he travelled to Pakistan four years ago. He was convicted last month and sentenced to death, and is now languishing in a seriously overcrowded prison in Rawalpindi.
His Pakistani counsel, who asked not to be named due to the sensitive nature of the case, said: "He remains entangled in his grandiose delusions and can make little sense of what is happening to him. He does not act like a man who has been sentenced to death, because he does not fully grasp what that means.
"Due to a lack of adequate medical or psychiatric care, he is not being treated for his mental illness nor is he being provided the treatment outlined by his Scottish psychiatrist."
Adiala Prison, where he is being held, "is grossly overcrowded with several inmates stuffed into a cell made to house two", she said.
A spokesman for the legal charity Reprieve said: "Mr Asghar remains a very ill man, and we're continuing to push the UK and Pakistani governments to work towards his speedy release to ensure he gets the medical attention he needs."
A Scottish Government spokesman said: "We are concerned about this case and are in contact with the Foreign & Commonwealth Office and Mr Asghar's family, who will keep us informed of the situation."