Nope, he didn't step up, He was in line with his partner Matip, and knew Kane was a good yard beyond him, so he assumed he was therefore offside when the ball went over, but Gomez had dropped off and played Kane on, that's why Lovren's first action when the ball went through was to glare at the lino, as he couldn't believe he hadn't flagged.
The second was 100% down to him though.
You could have the best CB in the World playing in that left CB berth, but with Moreno leaving him completely exposed every few minutes he'd still struggle.
Ok I get that Gomez is playing him onside what I mean is that there's no need for it, Lovren should just mark him. That might be down to Klopp but you have to manage yourself in the game and in that situation I just don't see the need to step up and even try an offside trap.

... I wonder if that had anything to do with