The Bianconeri bounced back from their second Serie A loss in the campaign - a 2-0 defeat at Napoli last time out - with a 1-0 triumph at Lyon in last week's first leg of their quarter-final tie.
Leonardo Bonucci's goal put Juve in command.
Elimination from the Europa League would be a major setback for Juve, who have high hopes of going all the way in the tournament this campaign, more so considering that the Juventus stadium is the venue for this year's final.
"Last year we were eliminated in the quarter-finals of the Champions League," Juve coach Antonio Conte said. "We are the only team alive in European competition and we want to go as far as possible.
"It would be fantastic to play the final in our stadium although we are still some way from that happening."
The immediate task for Juve is to return to winning ways after last weekend's setback in Naples.
Juve are eight points clear of Roma at the top of the Serie A standings with seven games remaining.
Conte could rest top scorer Carlos Tevez as a precaution in view of Thursday's crucial game against Lyon.
Tevez, who missed the encounter against Napoli through suspension, was forced to leave the pitch against Lyon early in the second half with a muscular problem.
Tests done on the Argentinian striker, who is Juve's top scorer with 18 goals, ruled out any serious damage.
Sebastian Giovinco is set to partner Fernando Llorente in attack against Livorno.
Livorno coach Domenico Di Carlo hopes his players can show the same battling display against Juve that saw them hold Inter Milan to a 2-2 draw last week.
The Tuscan outfit came from 2-0 down to earn a valuable point against Inter.
"My players never gave up hope and they showed a lot of character to get a result against Inter," Di Carlo said. "This is the approach we need when we go to Turin to face Juve.
"We still need to improve but we are on the right path."
Livorno are 18th in the standings, two points adrift of Bologna, who hold the last safety position.