In it, Cruickshank revealed he gave Lu an impromptu 25-minute reading session in a car park.
In the book he tells how he was unable to connect with the missing person but there was a good reason for it – because he wasn't dead.
The Sensing Murder medium declined to be interviewed.
In the book, Cruickshank writes how Mike's mother had been persistent in trying to get him to do a full reading, including approaching him at his motel and attending several of his shows.
Russell said his partner had talked to many psychics "to make sure Mike hadn't passed on".
"The psychics said Mike was living on an island," he said.
In her first public comment since Mike's disappearance, Lu told the Herald on Sunday last weekend she believed her son was alive and there was "not a single day I don't think of him. I love him deeply."
The family's extensive search for answers has seen them employ private investigator Mark Templeman, who has worked on high profile missing persons cases in New Zealand and overseas.
Russell revealed last weekend they had spent more than $150,000 on the search, including checking out a possible sighting of Mike and Beckenridge on Gili Air Island, Indonesia.
Police investigating the case have stated inquiries were "ongoing and this remains an active investigation".
"During the course of this investigation a variety of information has been received from the public and this information has been thoroughly assessed and investigated by the inquiry team," police said in a statement.
"As this inquiry remains an active police investigation the coroner's inquiry is on hold."