Having already captained France to glory at the 2018 World Cup in Russia, Lloris can complete an impressive double with victory over Liverpool on Saturday in Madrid.
Spurs produced a stunning comeback to squeeze past Ajax on away goals and set up an all-English final in Europe's premier club competition, with their goalkeeper honoured to be leading the side out at the Wanda Metropolitano.
"First of all, it's a privilege to be part of this successful team," Lloris said at a pre-match press conference.
"To win the World Cup was a massive achievement and it would not be possible without the help of my team-mates, and it's the case for the Champions League final.
"I feel like someone with a lot of privilege, but the most difficult thing is ahead of us - the game tomorrow.
"We want to put everything possible in to win it and to put a stamp on Champions League history."
Lloris highlighted the comeback win over Ajax, when they were 2-0 down at half-time in the second leg, as the best moment of his Spurs career - but hopes he can top that moment this weekend.
"The best example [of togetherness] was in Amsterdam after the game. This moment was one of the best moments in our Spurs career," the 32-year-old said.
"Obviously we want a better moment tomorrow after the game. As a professional athlete, I think it's important to enjoy the way you work."
Midfielder Harry Winks, meanwhile, believes Spurs' maiden appearance in the final is a testament to how far the club has progressed under Mauricio Pochettino.
"The occasion is massive, not only for everyone involved but also for the club and the fans," the England international told the media.
"It shows just how far Tottenham has come as a club. It's going to be a real special night for everyone involved and quite emotional for everybody."