I just took this flight to FCO last week. It left ATL 1 hr late, but arrived on time. It came in to a nice, new terminal in FCO that I had not been in before, but it required much walking. On the other hand, passport control was a breeze. No line, finished in 2-3 mins.

I suspect LH flies out of a different terminal, however, and getting there would present the main problem. If this is booked on separate tickets (and it sounds as if that's true) I wouldn't risk it myself.