The north London side were brilliant 3-1 winners against La Liga giants Real Madrid in the Champions League group stage on Wednesday night after goals from Dele Alli and Christian Eriksen.
Spurs lost 1-0 to title rivals Manchester United at Old Trafford last weekend after France international Anthony Martial scored an 81st-minute winner following his introduction off the bench.
Tottenham bounced back from the Old Trafford defeat with their 3-1 win against Champions League holders Real Madrid ahead of the visit of the Premier League’s basement club Crystal Palace.
Former Liverpool defender Lawrenson is confident Spurs will ease past Crystal Palace at the home of English football on Sunday afternoon.
“The confidence at Tottenham will be sky high after the performance and result against Real Madrid on Wednesday,” Lawrenson told BBC Sport.
“I don’t think there is any chance of a hangover from that victory with Mauricio Pochettino in charge. He is super prepared.
“Palace may still be bottom but their performances have improved under Roy Hodgson: they beat Chelsea, should have had a point at Newcastle and then got a dramatic draw against West Ham last week.
“He has improved them, but whether he can improve them enough remains to be seen. I look at Palace and I think ‘can they get enough points between now and 1 January – i.e. the transfer window – to give themselves a chance of attracting the players they think might keep them up?’
“I see Palace filling in the space at Wembley and making it difficult for Spurs, but I don’t see them creating any problems.”
Tottenham finished in second place in the Premier League last term after ending up seven points behind eventual champions Chelsea.
Spurs are in third place in the Premier League table and eight points behind current leaders Manchester City.
The north London side are looking to win the Premier League title for the first time to cap their progress under Argentinian coach Mauricio Pochettino.
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