That Barca team is widely seen as one of the best ever, and Lovren thinks the Reds can match their achievements this season and beyond.
"I've been there from the beginning with Jurgen and it took quite a while, two or three years to build everything up," Lovren told Sky Sports.
"Let's say, we clicked this year - maybe even last year - but we missed out by one point.
"Now we understand each other, what we need, what we want. And I especially want that we are remembered maybe like the Barcelona team that won in four years [about] 20 trophies.
"Why should we not do that? I think we can do it and I want that we are remembered as one of the best teams that have played - not only for this year, but for many, many years."