Lipsi island has ferry connection to Piraeus and to the surrounding islands:
Agathonisi (AGA), Kalymnos (KAL), Kos (KGS), Leros (LER), Patmos (PMS), Pythagoreio (PYT), Rodos (RHO), Symi (SYM),

You can also travel by plane to Kos,Kalymnos, Leros, or Samos, from where it is easy to catch a katamaran or ferry to your final destination of Lipsi.

Lipsi Port police +30-22470-41133
Leros port police +30-22470-22224
Patmos port police +30-22470-34131
Kalymnos port police +30-22430-29304-24444