We stayed for a week in apartment 6 (one bedroom) as a couple. The apartment was the perfect place to stay while exploring Lucerne and the region, being only a couple of minutes from the station and with all of the city within a short walking distance. We got our breakfast each morning from the bakery 30 seconds from the front door - ideal!
The hosts at Hotel Central were very friendly and welcoming, giving us a quick tour of the apartment and were helpful whenever we needed anything. They explained the cleaner comes once a week, halfway through our stay in our case, which worked well.
The apartment itself is well appointed, having been decorated recently with a modern design. We didn't cook anything elaborate but the kitchen was well equipped enough for our needs.
Lucerne was hot (~30C) when we visited, but the external shutters kept the apartment fairly cool, and we were given a fan by the hosts that meant we managed without issue.
The price was in-line with staying in a local hotel for a week, but the additional space and facilities made us much more comfortable. Overall I would strongly recommend Neustadt apartments to anyone staying in Lucerne and wouldn't hesitate to stay there again.