The former Spurs goalkeeper was delighted to see his old club end their 17-year wait for a trophy by winning last month's European showpiece against Manchester United and hopes that the triumph can relieve some of the pressure on the players.
Lloris, who now plies his trade for MLS side LAFC, said: "I am really pleased. I am really happy for the club, for the people at the club, for the players.
"We ran many, many years after this trophy and finally they got it and I think they deserve it.
"Hopefully it will make their shoulders a little bit lighter for the future and I think it is also the moment to build on this success for Spurs. Even if I am not a Spurs player, I still follow the news, the team and the results."
The trophy win was not enough to save manager Ange Postecoglou - who has been sacked and replaced by Thomas Frank - but Lloris wasn't shocked by the decision to dispense with the Australian coach's services after Spurs suffered a woeful Premier League campaign.
The former France international said: "No, nothing surprises me in football. But at the same time, it is hard to say something because I am on the other side. I don't know what happened inside the club so it really hard for me to judge.
"If they made this decision it is because they believe there is another option which is better for the future of the club.
"What Ange Postecoglou did was just remarkable. He brought this Europa League trophy, he brought a lot of joy to the Spurs community, a lot of pride as well and we all have to be thankful for that.
"I am not here to discuss about the choice [of Tottenham's new head coach]. He is a well-respected coach, He did an amazing job with Brentford. Now, like every coach, when you arrive in a new club, there is a new environment which you have to embrace. But if the club decided to appoint him, it is probably because they decide it is the best for the future."