Rhodes remains one of the more elegantly inconvenient prizes in the Aegean, and there is no single-carrier nonstop that spares you from connecting. Booking business class from Los Angeles to Rhodes today means routing through one of three credible gateways: London via British Airways, Frankfurt or Munich via Lufthansa, or Athens via Aegean Airlines, the latter being the only true specialist in Greek island connectivity. My preferred build has always been LAX–Frankfurt on Lufthansa, followed by a short Aegean hop into Rhodes International Airport (RHO), because Frankfurt's connection times to intra-European flights are generous and the terminal signage is mercifully clear even after a redeye. Total journey time hovers around 14.5 hours of flying, but budget closer to 18-20 hours door-to-door once you factor the layover.
Lufthansa's long-haul cabin out of LAX is worth planning around: on aircraft still running the older configuration you'll get their well-regarded business seat with direct aisle access, though the airline has begun rolling out Allegris on select routes, so it's worth checking your specific aircraft type at booking. British Airways, by contrast, routes you through Heathrow, and their Club Suite—with its sliding door and forward-facing layout—is genuinely one of the better products flying the Atlantic, making the London connection appealing even with Heathrow's notorious congestion; give yourself at least two hours there, particularly during summer. Aegean, while not a long-haul operator on this itinerary, deserves credit for consistently punctual short-haul service into Rhodes and a lounge in Athens that punches above its weight for a regional carrier.
The insider move is timing: April, May, September, and October not only avoid the punishing Aegean summer crowds at RHO's compact arrivals hall, but also align with when European carriers quietly release better business class award and revenue space as leisure demand softens. Because pricing on this three-airline, single-region route can swing significantly based on which hub has excess capacity that month, setting up fare alerts rather than checking manually will save you both money and second-guessing.