Kane is expected to miss the rest of the season due to ankle ligament damage suffered during Spurs’ 1-0 win over Manchester City 1-0 in the first leg of their Champions League quarter-final.
Dele Alli was also sidelined by a broken hand, while coach Mauricio Pochettino took the chance to rest some other key personnel such as 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 and a place in next season’s Champions League.
“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 might suffer a European 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.
And Pochettino was delighted to see his side rack up the score in the final stages with goal difference potentially pivotal come 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 move a point clear of Chelsea, who travel to title-chasing Liverpool on Sunday, while fifth-placed Arsenal are now 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 Champions League 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 still 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.
Brighton remain catchable for Neil Warnock’s men as they succumbed to a humiliating 5-0 home defeat to Bournemouth.
Eddie Howe’s side 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.
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 with 19 minutes left.
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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