Barbara's place is very clean and well-designed. While it is located on Lucca's main street adjacent to great shopping and dining options, it is unbelievably quiet. Nothing seems to be more than a ten minute walk away. It is located off an interior courtyard on the ground floor, so there is no need to lug suitcases upstairs.
Now, for the bad - there is no A/C - Apparently I missed this. If this is important to you, do not stay here. There is no airflow due to the location. The neighbors' exhaust also blows hot air into the courtyard raising the temperature even more - making opening the windows useless. Our stay was in August, so in cooler months, I could see having a much better experience. As it was, we were unable to make it even one night. At 10pm, the temperature was nearly 85F inside. We realized that this would likely be a problem upon check-in. I told Gaia that we didn't think that it would cool enough to be able to sleep. She told me to try, offered to bring a fan, and said that we could get a refund if not. (We never heard any more from her on the refund, although we did receive the posted standard amount from airbnb.) We were hot from the walk from the train station, (There are many stairs getting through the wall. If you have larger bags, take a taxi. It was approx. 12 Euros and well worth it.) so we decided to go shopping, get some gelato, have a spritz and return after dark. As soon as we returned, we realized that it was not going to cool before daybreak, so rather than endure a sweaty night, we left without having disturbed anything other than a bar of soup and a hand towel; and we found a nearby hotel which was lovely. Additionally, there is no wifi, which was fine, but I expected roaming to work; however I couldn't any signal, even to make a phone call (ATT).
Again, depending on the temperature, this place could be lovely. It has a lot going for it, and it is in the best part of Lucca. There was nothing that could be done for us, short of providing a fan, which was done. Barbara's other listings were booked or outside the city. Sadly, it was not the right fit for us.