Spurs have been impressive since Mauricio Pochettino took the reins in 2014 but silverware remains elusive for the North Londoners.
Club captain Lloris believes that next month's FA Cup semi-final against Manchester United is a chance for Spurs to show that they are ready "to step up a level".
"We want a trophy because I think we deserve a trophy," the France goalkeeper told The AP. "It's just because we play such attractive football.
"I think people enjoy the way we play because we are a very positive team with a lot of energy. The way we play football is a bit risky but we create a lot of chances.
"We need to step up a level every time that we can and we still have a good opportunity with the cup. I think we are going in the right way. We need to win trophies, obviously, but step by step we will arrive. We have no doubt about that."
Tottenham's last major trophy remains the 2008 League Cup.