The Spurs boss signed a short-term deal back in December to stay on until the end of the campaign, but Lawrenson does not think that owner Joe Lewis will retain the services of the current coach.
He told The Mirror: "[It was] a good win over Southampton [on Sunday] for Tim Sherwood but I'm convinced he will be gone in the summer. Spurs chairman Daniel Levy will be painted as the bad guy, just as he was when Harry Redknapp got the sack. But the decision won't be his.
"It will be that of owner Joe Lewis whether Sherwood gets Tottenham into the top four – against the odds – or not.
Spurs are currently fifth in the Premier League.