If you are arriving by car, you can travel to Lumbarda by ferry lines: Ploce - Trpanj - Orebic - Korcula; Orebic - Korcula; Drvenik - Korcula; Split - Vela Luka.
More on the ferry schedule can be found on www.jadrolinija.hr
Arrival by airplane
Airport Dubrovnik is 110 km away from Lumbarda. Airport Split - Kastele is 200 km away from Lumbarda. After landing at Split Airport or arriving by train to Split, you can catch a catamaran Split - Korčula.
More about air transport on the following websites: