This was definitely the best experience I could expect. The house is incredible, each appartement has it's own private area and the large terrace allows to meet people from all over the world.
Claudio and Paulo are perfect hosts, always happy to help with anything, they have picked me up and brought me to the ferry, rent their scooter for a day and cooked some delicious local food. They are also really helpful to show what real life is on the island and give tips for the stay.
Lipari is a great place to go around the islands, I've stayed 5 days and visited 5 islands. I did not rent a car nor walked to the city, I used the bus which is very convenient (1 every hour off season).