Getting from the Crescent City to the Cyclades in a lie-flat seat requires patience and smart routing, since there's no single-carrier nonstop solution for business class from New Orleans to Mykonos — every itinerary funnels through at least one major European or transatlantic hub before a final hop or ferry connection into JMK's compact, seasonal airport. The most reliable option pairs Lufthansa's transatlantic metal out of MSY-adjacent hubs like Atlanta or Houston (Louis Armstrong itself has limited direct widebody service, so many travelers position through Houston) with a Frankfurt or Munich connection, ideally booking into Lufthansa's new Allegris business class on routes where it's deployed, then continuing to Athens before a short intra-Greece hop on Aegean Airlines (A3) into Mykonos. British Airways offers another strong path via London Heathrow, where their Club Suite — with direct aisle access and a proper door — makes the long transatlantic leg feel considerably shorter before you connect onward to Athens and pick up an Aegean flight for the final island jump.
Having routed through Athens more times than I can count each summer, my advice is this: build in at least a three-hour buffer in ATH before your Aegean connection, since Mykonos-bound flights during peak July and August routinely shift gates and departure times due to the airport's constrained single-runway operations. A better-kept secret is flying into Mykonos in early June or mid-September, when Aegean adds extra frequencies but crowds and heat are far more manageable — and when premium fares on the transatlantic legs tend to soften considerably. Aegean's business class on these short intra-Greek hops is more regional-comfort than aspirational product, so treat it as a scenic finale rather than the main event; the real luxury investment goes into your transatlantic segment.
April, May, September, and October consistently deliver the best value for this itinerary, as European carriers adjust business class award and revenue inventory ahead of and after the peak Aegean tourist crush. Given how much these fares fluctuate based on Lufthansa and British Airways schedule changes into Athens, setting up automated fare alerts is genuinely the smartest way to catch a premium seat to Mykonos before prices firm up for summer.