The former Anfield defender believes the breakdown in trust between the Liverpool manager and chief executive Rick Parry would make it difficult for Benitez to land the players he wants in the summer transfer market.
It was revealed in reports this week that Parry had a hand in talks with Jurgen Klinsmann last November, along with warring co-owners Tom Hicks and George Gillett.
Asked if Benitez would be there next season, Lawrenson said: “If they don’t sort the mess out soon I’d have to think he would not be, regardless of whether they win the Champions League.
“The problems off the pitch could give him an excuse to leave. If they win the Champions League there would be no shortage of takers and he probably thinks ‘why should I turn up and flog my guts out for this lot when I don’t know what is going to happen next week?’
“He must come in every day and wonder what he is going to read about that he didn’t know.”
Lawrenson, who played 241 times for Liverpool in the 1980s, including the FA Cup final against Everton in 1986, admits he has been saddened by the squabbling between Hicks and Gillett and believes the club would be better served by the Dubai consortium DIC who are eager to take over.
He said: “(Bill Shankly) Shanks, Bob Paisley, Joe Fagan must be turning in their graves when you consider what they did for the football club.
“It’s an everyday farce and credit goes to the manager and the players.”
“The sooner someone can get Hicks and Gillett round the table and sort out who pays who off and who retains the majority in the football club and lets the Dubai people in the better.”