General complaints I've heard about him stem from both the bad pacing of Batman Eternal and RHATO fans despising his run on the comic.
For the former, I think that was forgivable when you look at it as an inexperienced writer overseeing such a large project, which I think is clearly rectified in Batman and Robin Eternal right now, while the latter is a run I actually liked, but seems to be rejected by the majority of the online fans.
I tend to disagree with them since I thought Tynion gave us a great Cheshire and Arsenal relationship, a storyline where Ra's Al Ghul came out on top in a story featuring Image character rejects I never cared for in the first place, and my general tastes running more in line with Tynion's writing than Lobdell's. I mean, I still thought the arc was pretty flawed, but...I still felt that flawed arc was far more engaging and interesting than anything else Lobdell dropped on it outside of a few standalone issues.
Of course, I've also got a massive bias against Lobdell, since aim actually a fan of Tim Drake, Superboy, Bart Allen, and Wondergirl, and I think he, at best, was very much the wrong writer for a job that was going to be screwed over a little bit by editorial no matter what, and that his best stuff in the New 52 is piddly; I'll admit he clearly knows how to right Jason and Roy, but his plots still strike me as uninspired and generally boring, while Tynion strikes me as the opposite, favoring bigger and more interesting plots marred by a heavy handed characterization.
But hey, at least Tynion can write a Tim Drake and a Jason Todd in a fun story with a generally threatening villain. That's more than I've thought Lobdell can do.