Di Livio, who amassed 269 appearances for Juventus between 1993-99 as well as 40 Italy caps, think Juve are "still far away" from being UEFA Champions League contenders.
“They’ve also found it difficult in the league and, in fact, a super Lazio have resurfaced, only a point behind," Di Livio said to Corriere dello Sport. "They risk [throwing both tournaments away].
“In the Champions League with Lyon they have a result to overturn, but I didn’t like their mentality very much.
“Aggression, a ruthless streak and attachment to the shirt are all currently missing. They seem a bit sluggish to me this season.”
Di Livio, who won the Champions League under Lippi in 1996 as well as three Serie A titles, also said the decision to replace successful coach Allegri with Maurizio Sarri was hard to comprehend.
“It was a change only a few people understood," said the former midfielder.
"Anyone who wins must always be respected and can’t be sent away. Allegri will be the new Lippi.
"My best wishes go out to Sarri, who has understood what it feels like to be at a side where you always have to win.”
Juventus are 1-0 down against Lyon after the first leg of their Champions League round of 16 clash, while they lead the Serie A table just one point ahead of high-flying Lazio.
