The Bianconeri are unbeaten in their last seven games in the competition.
Their next game is Saturday against the reigning champions.
The Biancones beat Juventus 2-1 at the Stadio Olimpico on Monday to reach the quarter-finals.
Juventus were beaten 1-0 by Napoli on Tuesday.
“I am proud of this team and its supporters, and I think they are very hungry,” Juventus manager Massimiliano Allegri said.
It was the third consecutive defeat for the Nerazzurri, who have won their last two games against Roma and Lazio.
Ancelotti has not won in Italy since beating Bayern Munich 2-0 on March 14, 2002.
He will lead a side who have only lost one game in the Europa League since March 12, 2018, when they drew 2-2 with FC Augsburg in the final.
Lazio have not won at home in the league since the last meeting in the Coppa Italia final on March 9, 2016, when the Bianconero beat Sampdoria.
Allegri said he would use his experience of the past two matches to “make a good team.”
“We will have a good understanding of what it is like to play here,” he said.
“We will play with more energy, a bit more of a purpose, a little more passion.
We will make sure we will get the points.
We have to be more patient, but we have to keep pushing.”
Alvaro Morata scored twice for Juventus in their previous Champions League encounter against Roma in April.
They lost 2-3 in the second leg.
Villa boss Roberto Mancini is also under pressure to improve his side’s attacking options.
Roma coach Antonio Conte is the last coach to win two Serie A titles with the same team in his first season in charge.
Domenico Berardi’s side lost 4-1 to Napoli in their opening Champions League match.
Barca lost 2 – 1 to Sampdori in the last game of the season in the first leg of their Champions League play-off.
Former Inter Milan and Sampdora boss Giampaolo Pazzini’s side have lost three of their last four matches in Serie A. “There are some players that are not good enough, there are some that are out of shape,” Allegri told Sky Sport Italia.
“It is a difficult situation and we are trying to help them.”
Juve have won three of four meetings with Lazio in the Serie A table, with their only defeat coming at the San Siro.
Napoli have won two of their past three matches, but Allegri was not overly concerned about them against Juventus.
‘Juve won’t win this game’ “It is going to be difficult, it is going the way they want it to be,” he added.
“They have won the last two meetings against them, and it is always difficult for us.
They are a very good team.
We will win this one.”
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