Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Honolulu to Limassol as you normally would.
Located just 4.4 mi from the city center, Honolulu is the airport most travelers will use when flying to Limassol from Honolulu. Booking flights from Honolulu (HNL) to Limassol should be relatively easy as there are 0 daily outbound flights to Limassol from 0 different airlines.
HNL and LCA are unique codes to identify airports used in the aviation industry. They are defined by IATA (International Air Transport Association) and are commonly called IATA codes. HNL to LCA refers to a flight route from Honolulu Airport to Larnaca Airport. Paphos Airport (PFO), Nicosia Ercan Airport (ECN) are other airports near this flight route and their unique identifiers/IATA codes.