A good tactic/team set-up makes everyone look good. And a bad set-up makes everyone look bad. Both are at play here. Lovren doesn't have the same help from the midfield at Liverpool. It seems to me like the player/position that Liverpool really needed to replace was Gerrard. But because of his iconic status, they spent on every position EXCEPT that one.. on players they didn't necessarily need or aren't that good.
LFC is completely disorganized at the back as well. Lovren took a huge knock from his own player on a nothing ball; there was no reason for two players to even get bunched up going for that ball, much less fail to communicate so badly they collide.
Their defense was a little shaky last year. But rather than fix the problem via coaching by adjusting tactics or emphasizing defense in practice or something, I think they just decided they'd sign Lovren as a magic fix.