Kane is expected to miss the rest of the season due to ankle ligament damage suffered in the victory over Manchester City 1-0 in the first leg of a Champions League quarter-final in midweek.
Dele Alli was also sidelined by a broken hand, while Mauricio Pochettino took the chance to rest some other key personnel, including Son Heung-min, ahead of the second leg against City on Wednesday.
Lucas took his chance to shine against the already relegated Terriers to show Pochettino he could be an important weapon in Kane’s absence as Spurs look to tie down a top-four finish.
“Players need to play to show their quality. The hat-trick is going to build his confidence,” said Pochettino.
Victor Wanyama opened the scoring on 24 minutes to allay any fears that Tottenham could suffer a Champions League hangover.
Lucas made it 2-0 three minutes later and then struck twice more in the final three minutes as Pochettino’s men made it three wins from three at their impressive new 62,000 capacity home.
Pochettino was delighted to see his side rack up the score in the final stages with goal difference potentially pivotal come to the end of the season.
“It is going to be a very tough race. To score several goals is important. The goal difference can be decisive to achieve the top four at the end,” added the Argentine.
Tottenham moves a point clear of Chelsea, who travel to title-chasing Liverpool on Sunday, while fifth-placed Arsenal are four points adrift of their north London rivals but have a game in hand at Watford on Monday.
Controversial Cardiff defeat
While the title and fight for top-four places look set to go down to the wire, the relegation battle could be all but over should Brighton beat Cardiff on Tuesday.
The Welsh side are five points adrift of safety after a controversial defeat at Turf Moor.
Chris Wood gave the hosts a deserved half-time lead, but Cardiff were left furious after referee Mike Dean overruled his assistant’s decision to award a penalty to the visitors after the break.
Another big Cardiff penalty appeal was turned down before Wood sealed the win in stoppage time.
“There were two handballs really, you only have to look at the players reaction – he looked so guilty,” said Cardiff manager Neil Warnock. “The second one we felt there was a movement of the hand towards the ball.”
Brighton remain catchable for Neil Warnock’s men as they succumbed to a humiliating 5-0 home defeat to Bournemouth.
The Cherries had lost 11 of their last 12 games on the road, but moved up to 12th thanks to goals from Dan Gosling, Ryan Fraser, David Brooks, Callum Wilson and Junior Stanislas.
A dreadful day for the Seagulls was rounded off by a red card for Anthony Knockaert.
“We’ve got to get back to being the solid team we know we can be,” said Brighton boss Chris Hughton. “If we thought today was a big game then Tuesday is an even bigger one.”
Southampton further eased their relegation fears with a 3-1 win over Wolves to move eight points clear of the drop zone.
Nathan Redmond scored twice either side of Willy Boly’s equaliser in the first-half before Shane Long sealed a vital three points.
Fulham’s relegation to the Championship is already assured, but they secured just a fifth win of the season by beating Everton 2-0 thanks to second-half goals from Tom Cairney and Ryan Babel.
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