Lawrenson recalls: "I had agreed a deal with Graeme Souness to buy Jimmy Phillips, who's now at Bolton, from Rangers. Kevin was on the boat, the one Robert [Maxwell] was on when he died. I rang ship-to-shore and the voice at the other end was Robert who was then chairman of Derby County."
Lawrenson then does a passable impression of Maxwell's famous booming voice as he relates: "He said `Hello'. I said `Mr Maxwell, it's Mark Lawrenson, can I speak to Kevin?'
`Speak to me.'
`Well, it involves one of our players.'
`Speak to me.'
`Well, Kevin's my chairman.'
`Speak to me.'
"I spoke to him," Lawrenson said. "I told him about Phillips and he went: `Done.' So the Derby County chairman had just agreed for Oxford United to buy a full-back from Glasgow Rangers. That," added Lawrenson, "just about summed up the situation."
No wonder Lawrenson agreed when Kevin Keegan asked him to work with Newcastle United's defence. After dealing with the Maxwells even the prospect of getting David Ginola to defend cannot seem that daunting.
"I'm enjoying it. It is nice to be back in the game - and in this capacity. I didn't expect it. I'd carved out my own career in the media."
We were talking in Vienna where Lawrenson was preparing to work for BBC Radio at Manchester United's Champions' League tie with Rapid Vienna. His media work also includes Sky TV and a newspaper column.
Newcastle is the priority. The previous night he had watched them beat Metz in the Uefa Cup and, when we returned to Manchester Airport in the early hours of Thursday morning he drove straight to his new home in Gosforth to help prepare for Monday's match with Nottingham Forest.
"It was a surprise," he recalled. "I went up to do an interview with Keith Gillespie for Sky. As we were doing it a story broke about [Faustino] Asprilla being late back so I asked Kevin a few questions on that.
"The following day I got a message to ring Terry McDermott urgently. I thought, `Oh no. They're objecting to something we asked.' When Terry said `Kevin wants to speak to you' I was sure they were. Then Kevin asked if I wanted `to get back in it'.
"I am primarily involved with the defenders though I speak to all the players. I have not really worked with them, it is more a case of trying to make salient points. They now come to me after a game and ask about certain incidents, what they did, what they should have done. They have responded which is great when you consider I was one of their fiercest critics."
Lawrenson, like Keegan, does not use video - "players always know exactly what happened" - but he has had to get used to supporters watching training. "In a way it helps. You have always got the players' attention. They know they are on show."
There is also Keegan's current penchant for playing three centre-backs and attacking wing-backs to deal with.
"Kevin likes to think there are not many teams playing with wingers, why not play that way? It gives us width, inventiveness and numbers in midfield which help us win the ball back when we lose it. It is a case of making everybody aware of their responsibilities.
"A lot falls upon the two wing-backs. We are trying to convince Ginola that it is the way to play. He has never played that way before and I think he finds it difficult, when people run past him, to have to track them back. On Tuesday he did it well for us. We know we are not going to get him running 50 yards and slide in and make a tackle. What we are saying to him is that when we lose the ball make sure you run back 10 yards to save yourself running 40 later on. If the full-back is aware that you are going to go with him he is going to stop going after a while."
A quick run through the video suggests Ginola did track back more against Metz than Arsenal but there were times when his lack of defensive nous was exposed. "It does not come automatically to him as it has done to Gillespie," Lawrenson admitted. "There are times when he thinks that maybe it detracts from him going forward but it should not do, it is a good system."
More generally, said Lawrenson, his aim is to "make them think pessimistically" - the what-if syndrome. "Ultimately you are trying to get them to prevent danger rather than react to it. The good defenders are the ones who make sure there is not a problem in the first place.
"In Europe you have to be very patient. Attackers are used to playing against man-markers and they look to pull you out of position. All we say to people like [Philippe] Albert and [Darren] Peacock is that, 99 per cent of the time, if you don't get pulled out of position we should be OK."
One thing Lawrenson does not tell his pupils is how Liverpool did it. "We never talk about it, not to players. It does not have any relevance and if you don't, I think players respect you more. Kevin, Terry and I might tell a few stories to ourselves, "do you remember when", but very rarely do we say "if that had been Liverpool in the 80s..."
Lawrenson did not play with Keegan but is credited for persuading him to retire. Keegan went back to Anfield with Newcastle for an FA Cup tie in 1984 and was comprehensively outpaced by Lawrenson. Afterwards he decided it was his last season. "Maybe this is his way of getting revenge," Lawrenson said.
Lawrenson, who also played for Preston, Brighton and the Republic of Ireland (38 caps) retired at 30 with an Achilles tendon injury in 1988. While Liverpool went on to be champions, he took over at relegation-bound Oxford making him the answer to the teaser: who won a championship medal and was relegated in the same season? (He once asked this question of the press corps then enjoyed the many wrong answers before someone realised.)
He was at Oxford seven months. "It was an experience and an education," he said. "I'm glad I did it. In a surreal way I enjoyed it. I don't know if there will be the like of Robert Maxwell again.
"I dealt with Kevin but when there was a major decision it obviously went to his father. I would ring Kevin up about trying to sign someone and he would say `I will get back to you'. And he spoke to dad. As part of the empire it was understandable.
"The thing I learned straight away was that whatever Robert Maxwell did he had to think he was getting a deal. So if I needed pounds 200,000 to buy a player I had to get the message through that they were asking for pounds 300,000."
The relationship was never likely to prosper and Lawrenson left when Dean Saunders was sold against his will - after Lawrenson had been promised he could keep him for the season and told season-ticket buyers the same.
"He went in October, we were seventh and at home to Blackburn. I arrived and Kevin told me, `I know what we agreed but Saunders has to speak to Derby after the game'. Obviously his dad had been on. Derby had been on the phone a few times about Saunders but others fancied him too.
"Dean signed that night. I voiced my opinion to Kevin and he said `speak to my father'. The next day I went up to the penthouse at the Mirror building. He sat right next to me, very close, on a Chinese inlaid coffee table. It looked very expensive and it started to buckle. I thought `this could be funny, if it was not for the situation it could be very funny'.
"He said: `What's your problem young man?' I said: `You know what my problem is' and came out with all this rhetoric about Saunders and promises to me and the season-ticket holders. He said, `It's got nothing to do with you' and walked out.
"I went home and decided to resign. The next day I went back with Brian Horton, my assistant. He was whisked off straight away to be offered the job (I'd already told him to take it if they did). I'm kept waiting for an hour. Kevin walked in, threw this piece of paper at me and told me I was being sacked for telling the press I was resigning - which was not true. I said, `If you're happy throwing that at me, I'm sorry'. His parting shot was, `Nobody resigns on Robert Maxwell.'"
Lawrenson's most surprising tale is a confession. "The best thing to happen to me in football was signing for Preston. I was born in and went to school in Preston, my dad played for Preston, my stepfather was a director, my mother had watched Preston for most of her life. The day I played for the first team was probably the best.
"Liverpool supporters say `How can you say that? You won the League five times, you won the European Cup'. But, from the age of four or five, that was all I ever wanted. The rest was a bonus."