Lufthansa is trying to improve its long haul passenger experience. One major component of that is the debut of new Allegris cabins , which includes a new first class and new business class . On top of that, it includes the introduction of the FOX (“Future Onboard Experience”) service concept , whereby service across all cabins is being overhauled, regardless of whether flights are operated by planes with Allegris interiors or not. In a separate post, I broadly covered the changes that are being promised . The new first class soft product rolled out in late March, while the new soft product in other cabins is debuting this week. Over the weekend, I had the chance to fly Lufthansa first class from Frankfurt (FRA) to New York (JFK), a flight that was operated by the A340-600.…