There is no nonstop path to this Ionian island, which is precisely what makes booking business class from Los Angeles to Zakynthos an exercise in routing strategy rather than a simple search. The most reliable itinerary runs through Munich or Frankfurt on Lufthansa before a connection onward via Athens on Aegean Airlines, since Zakynthos itself has no long-haul capable runway and every business-class journey terminates in a regional hop. Lufthansa's transatlantic legs out of LAX increasingly feature the new Allegris business suite with a closing door, though not every aircraft has been retrofitted yet, so it's worth checking the specific tail assignment before booking. British Airways offers an alternative via London Heathrow, where the Club Suite's direct-aisle-access seat makes the long crossing genuinely restful, followed by a shorter connection down to Athens and a same-day Aegean flight to Zakynthos on an A320-family jet.
Having flown this corridor across several seasons, I've found the Munich connection superior to Heathrow for tight layovers, since Munich's efficient transfer process between the Schengen zone and the Aegean flight gives you more breathing room than LHR's often-congested Terminal 5 to Terminal 3 shuffle when connecting to non-oneworld metal. The insider move: book the final Athens–Zakynthos segment as a separate Aegean ticket with generous connection time, because seasonal Ionian weather in early spring and late autumn can delay short-hop turboprop and regional jet operations, and you don't want a missed connection unraveling your long-haul business fare. April, May, September, and October remain the sweet spot — not just for lighter crowds on Zakynthos's beaches, but because carriers historically loosen premium cabin award and revenue pricing before and after the July-August surge.
Given how fragmented this routing is, fares fluctuate more than on typical transatlantic city pairs, so setting up fare alerts across the LAX–MUC–ATH–ZTH and LAX–LHR–ATH–ZTH combinations will do more for your wallet than any single booking trick.