Great B&B in the center of Lipari town. Cheap, clean, nicely decorated and serves a good breakfast in the open terrace upstairs.
Owners very helpful, they'll pick you up in the port if you let them know in which ferry you're arriving.
We've found that other people looking for this hotel also know it by these names:
Address: Vico Himera 3, Lipari, 98055, Italy