I strongly recommend this place -- we stayed for over 2 weeks and enjoyed it immensely.
The location is almost ridiculously convenient, walking distance to lots of sites, and a main drag was just a block away, where you could catch buses to almost anywhere in town. There's a little market next door run by another Lorenzo, who was very friendly and speaks good English, plus a couple of restaurants just steps away. And yet it was not at all noisy, even tho you're on the ground floor. Also, I didn't get the slightest vibe of insecurity -- the whole area felt completely safe.
Any downsides were probably unavoidable because of the location in an old building in the historic center. We were quite comfortable as 2 people, but it could get cramped for more. The washer worked fine, but was tiny. The AC unit in the living room seemed to work better than the one in the bedroom. Also, wifi was great in the living room but was spotty in the bedroom, probably because of the stone walls.
Communication with Lorenzo (the apartment owner, not the guy at the little market) was excellent -- quick responses and quick action.
If you're the type who needs room service and massages, this is not the place for you. But if you want to actually see Rome, this is the place you want to stay.