The Lilywhites have made a mixed start to the season at Wembley, as they play their home games at the national stadium while White Hart Lane is redeveloped this season.
Spurs have not yet won in the Premier League at Wembley after having dropped points against Chelsea and Burnley in north London.
However, Tottenham have been in good form on the road in the Premier League, picking up wins at Newcastle United and Everton.
Spurs also got their Champions League campaign off to an impressive start at Wembley last week with a 3-1 victory over Bundesliga side Dortmund in their group stage opener.
And former Liverpool man Lawrenson is tipping the Lilywhites to claim their first Premier League victory of the season at the national stadium on Saturday evening.
Lawrenson wrote in his column for BBC Sport: “The way Tottenham dismantled Everton last week was very impressive.
“In contrast, Swansea really struggled against Newcastle.
“After seeing the Swans beat Crystal Palace, I was not too worried about Paul Clement’s side getting dragged into the relegation battle this season – but any more complete non-performances like that would be a real cause for concern.
“Much has been made of Spurs’ poor record at Wembley until they beat Borussia Dortmund on Wednesday.
“But even if they had stayed at White Hart Lane, it would have been a huge ask for them to repeat their results there last season when they won 17 and drew two of their 19 home league games.
“This is the kind of game I would expect Spurs to win comfortably, regardless of the venue.”
Tottenham were Chelsea’s closest challengers for the Premier League title last season as they finished second in the table after an impressive campaign.
The Lilywhites head into this weekend’s round of fixtures in fifth place in the Premier League table after four games.
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