A 2-2 draw in Turin last month means Tottenham are favourites to progress to the quarter-finals after Wednesday night's last-16 second-leg game at Wembley Stadium.
"It's true we have a small advantage because we scored two goals away from home," Lloris, who conceded twice in the opening 10 minutes of the first leg, told a news conference on Tuesday.
"But if you don't have the right energy, the right mentality and the right attitude things can turn very quickly."
He added: "I think we have arrived at the point where we have maturity and we know exactly the expectation from the manager and how he wants us to play football.
"Now it's just to enjoy because we are in the period of the season where we can win and lose everything we have worked for.
"We are in good shape, mentally and physically strong and we have good opportunity tomorrow against one of the biggest clubs in Europe. It's a great moment to show the real face of Tottenham, the state today of the team and the club."