England Under-21 international Kane has been in superb form so far this season and has been one of the best young players in the Premier League.
The 21-year-old has scored 20 goals in all competitions already, including 10 in the Premier League.
Kane started the 2014-15 campaign as the third-choice striker for Spurs behind Roberto Soldado and Emmanuel Adebayor, but he is now on the first names on the teamsheet.
The youngster’s impressive performances have not gone unnoticed by Lawrenson, who has been effusive in his praise of him on BBC Sport.
“Harry Kane is the story of the season for Tottenham,” wrote the 57-year-old. “His development has been staggering and he is a guy who has really forced his way through. In a matter of months he has gone from back-up striker to the first name on the team-sheet.
“Earlier in the campaign, I got the impression that Spurs boss Mauricio Pochettino did not really trust Kane in the way his side play, which is with Christian Eriksen behind a sole striker.
“Maybe Pochettino did not think Kane was ready for that. But boy, is he ever. He has been outstanding.”
On Saturday’s match, Lawrenson added: “Like Spurs, Arsenal are going really well and they have both got serious designs on the top four. Because they are both in such good form, I think this is going to end up in a draw.”
Could Lawrenson’s prediction come true?
Saturday’s match at White Hart Lane promises to be hugely competitive and entertaining, and it is very much possible that the two sides will eventually have to settle for a share of the spoils.
Both Tottenham and Arsenal will head into the game on the back of comprehensive wins last weekend, but Mauricio Pochettino’s team will have an advantage as they are at home.
One suspects that the first goal will be key in shaping the tone of the game and the final outcome.