Goals from Jamie Vardy, Riyad Mahrez and Kelechi Iheanacho had put the Foxes into a 3-1 lead by the 47th minute at Wembley.
Two minutes after Iheanacho's effort, Lamela got his first league goal since August 2016 when he tapped home from Kyle Walker-Peters' low cross at the end of a neat move.
A draw would have dropped Tottenham below Liverpool into fourth spot but Kane had the final say when he cut in from the left to curl a trademark effort past Leicester goalkeeper Eldin Jakupovic. Liverpool in CL Liverpool cruised back into the Champions League next season by easing past Brighton 4-0 on Sunday as Mohamed Salah set a new Premier League record of 32 goals in a 38- game season.
It remains to be seen if boss Mauricio Pochettino and key centre-back Toby Alderweireld, who have both been the subject of speculation surrounding their futures, will remain with Spurs when they leave the national stadium to play at their new ground on the site of the old White Hart Lane next season.
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And Pochettino's side made no mistake as they ran out 5-4 winners in a insane game against Leicester City at Wembley.
There was absolutely nothing Lloris could do about Iheanacho's stunning strike that did extend Leicester's lead two minutes after the restart.
Vardy then made it 4-4 as Mahrez timed his pass perfectly and Vardy smashed home his 20th goal of the PL season in style.
Leicester City manager Claude Puel has insisted that his side should have beaten Tottenham Hotspur at Wembley Stadium after scoring four goals there.
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- Harry Kane has scored more goals in all competitions versus Leicester City than against any other side in his career (13).
"Of course, I want to retain the boot but consistency is the most important thing for me, getting 25-plus goals in the Premier League season after season".
- Harry Kane is the first Spurs player to score 40+ goals in a season in all competitions since Clive Allen in 1986-87 (49).
His tally of 30 league goals is the highest of his career so far and he became only the seventh player in Europe's top five...
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"It's insane to lose a game where you've scored four goals away", Puel added.