The Naples to Lipari hydrofoil service terminates on September 30 and will resume again at the end of May, 2008.
For the last week of September, your ONLY hydrofoil operator is Ustica Lines
www.usticalines.itDeparture Naples 8:00 (daily through Sept. 30)
Arrival Lipari 13:40
One way fare: 74.90 Euros plus 2.51 Euros taxes and supplement
There is also the twice weekly SIREMAR overnight car ferry on Tuesdays and Fridays.
www.siremar.itFinally, if neither the hydrofoil nor the ferry schedules are convenient, you can take the daylight or overnight train from Naples to Milazzo, then proceed to Lipari by hydrofoil (Siremar and Ustica Lines) or car ferry (Siremar only).
You won't need reservations for this run because Sept. 23 is already past high season.
P.S.: I think that the Lipari National Archeological Museum is great: I've been there four times in four years.
As Anastasia notes, you can also take the Ustica Lines hydrofoil from Vulcano/Lipari to Cefalu (bypassing Milazzo), three times weekly (Monday-Friday-Sunday morning) at the end of September. One way fare from Vulcano to Cefalu is 22.20 Euros. Travel time is 3.5 hours. The hydrofoil stops at Lipari, Salina, Filicudi and Alicudi, then proceeds to Cefalu and Palermo.
Hydrofoil service is subject to cancellation due to poor weather.