Spurs are currently in fourth place in the Premier League table as Mauricio Pochettino looks to guide the north London side back into the Champions League.
The Lilywhites returned to winning ways with a 2-0 victory at Southampton last weekend following their surprise defeat by Newcastle United at White Hart Lane earlier this month.
And former Liverpool man Lawrenson feels that the home side will have too much for the visiting Canaries on Boxing Day.
Lawrenson told BBC Sport: “After seeing Spurs throw away a lead to lose 2-1 against Newcastle, I thought the trip to Southampton on Saturday would show how mentally tough they are. They proved it and I think they are ready for top four.
“Harry Kane has scored eight in his past eight league games, we know about Dele Alli’s attributes, fellow midfielder Mousa Dembele is starting to play, and they are solid at the back as well.
“Norwich beat Manchester United at Old Trafford to record their best result for many a year. It was a very good display and they deserved to win. But they didn’t get questioned by United until the last 20 minutes – Spurs will ask questions for 90 minutes.”
Tottenham, who are one goal away from their 100th against Norwich in all competitions, have lost just one of their last 16 Premier League matches this season.
Spurs spent Christmas Day in the top four for the first time since 2011-12 – when they last finished in the Champions League places.
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