The World Cup-winning captain was arrested and charged by police last month and today admitted being more than two times over the legal limit.
Lloris has subsequently been fined £50,000 by the court and banned from driving for 20 months, and the Evening Standard reports that the club will impose further sanctions on him internally.
Spurs are expected to dish out the maximum club fine of over £250,000 - the equivalent of two weeks' wages - although manager Mauricio Pochettino has previously played down the possibility of stripping him of the Tottenham captaincy.
Westminster Magistrates' Court heard that Lloris had to be helped out of his £115,000 Porsche and was unsteady on his feet and slurring when stopped by police.
The France international - who was carrying a passenger - was seen veering across the road in London, almost hitting parked cars and then running a red light when stopped by police.
Lloris has missed the last three matches for club and country, although that is down to a thigh injury rather than the drink-driving offence.