You can travel to Lipsi by ferry boat from  Patmos or Leros and then on to Lipsi by local boats or catamarans daily.  There is also a direct link from Pireaus port (Athens) once a week.

One may choose to travel by air to Leros, Kalymnos, Samos or Kos and then to Lipsi by boats the same day.

There are daily connections with  Patmos, Leros, Kalymnos, Samos, Kos and Rhodes.

Airlines: Aegean Airlines, Lufthansa
Ferry Lines: Ferries, gtp, openseas, Blue Star Ferries,
Local Ferry lines: Catamaran