He's poor alright, the unit is poor though so it's difficult to say whether the keeper would be better behind a stronger defense, or the back four would be stronger ahead of a stable keeper. They all suck at the minute.
As for Lovren pushing out to attack the ball and to get tight to people, he's getting caught flat footed alot, if he doesn't get there (and it's happening alot) then we get caught in behind and Skrtel becomes isolated. It's not really as simple as them both stepping up because Lovren is (typlically) doing the work of the stopper, while Skrtel is being employed to mop up. In that sense they should compliment eachother, but it's just not working because the timing and concentration isn't there and we lack anything resembling cohesion as a unit. The fact they are so wide apart, from a starting attacking stance, isn't helping one bit, because we find it so difficult to regroup, which is understandable to a degree.
Rodgers needs a serious rethink, because the more we lack goals in games, the more we throw people forward and the less unified we become as a team when on the back foot, it's proving piss easy to exploit. That's a systematic issue, the chronic inability to defend a cross/setpiece into the box is inexcusable.