My husband and I just spent 6 nights at Lorenzo's. In addition to all the wonderful things other people said that we agree with, I want to add a few notes:
1. The terrace was our peaceful haven where we had wine, cheese and bread in the evenings after a long day of sightseeing with the crowds. The terrace is just big enough for two and looks over several other terraces, where we'd sometimes see or hear other airbnb'ers and sometimes locals hanging their laundry or talking.
2. If you are a security freak like my husband, this is the place for you! The street door is thick and secure. Then up on the second floor, the door to the apartment is also heavy, with a skeleton key that forces metal rods into the ceiling and floor to secure the door closed. No one is breaking in to Lorenzo's place.
3. We live in the country and wondered if city noises would keep us awake. No! Lorenzo's place is super quiet, so we had great sleep. (We did hear neighbors coming in and out of their apartments a bit, but then all quiet.)
4. We can't say enough about the neighborhood of Monti. While there were certainly tourists at the restaurants and on the streets, most of the people we came in contact with were local. After dinner you have to hang out with an aperol spritz at the Piazza della Madonna dei Monti, just a couple of blocks from Lorenzo's!