There is no doubt about Liverpool performance in this season as they are currently badly down in English Premier League, but their performance in Champions League is surely at their best, and they can do better after this break in knock out round which could be change things drastically for them with now two months break is surely going to have better change for them, and they can work on their weakness which is surely hurting them in this season.
Klopp which is here for long time will surely improve performance and quality for having better end of this season because right now situation is surely not good for them in Premier League they have to done good work if they want to enjoy good and successful end of this season.
With an unstable performance plus many players who were absent due to injury, Liverpool had to desperately play their match in the group phase of this competition. fortunately, Liverpool's opponent in the Champions League group stage was not too tough. only Napoli, who gave them a surprise at the start of this competition. however, if Klopp can't rebuild his squad's performance back to its true form. I doubt Liverpool can advance to the next round with such an unstable performance.
the reason is, there are many who will become more solid and tough opponents in the round of 16 later. however, as you said. having a break of two months will bring changes for the better for them, they can recover the mentality and fatigue that has been a barrier. even so, after all there is a team that has a higher probability of being favorites in this competition.
one of them is Bayern Munich, which looks like it will be difficult to beat whoever the opponent later.