There's no nonstop path linking New Mexico to the Grand Duchy, which means every itinerary in business class from Albuquerque to Luxembourg routes through at least one major hub, and after years of testing these connections, I've settled on Atlanta or Detroit via Delta as the most reliable start, feeding into transatlantic metal or a Delta One codeshare, versus a Lufthansa routing through Frankfurt or Munich that gets you onto Luxair's short regional hop into Findel Airport. The truth is Luxembourg has no widebody long-haul service of its own, so Luxair (LG) exists purely as that final European connector, and the real business-class decision happens on the transatlantic leg: Delta One Suites with sliding privacy doors on 767s and A330s/A350s out of the Atlanta or JFK gateways, or Lufthansa's business class (increasingly the new Allegris cabin on select 787 and A350 routes) into Frankfurt, where the connection to LUX is short and efficient if you clear immigration early.
My strong preference after many trips is routing via Frankfurt rather than Atlanta when timing allows, because Frankfurt's Lufthansa business lounges (particularly the First Class Lounge if your itinerary or status permits access) make a long layover genuinely restorative, whereas Atlanta's connection windows are tighter and less forgiving if the inbound flight from Albuquerque runs late. One insider tip: book the Albuquerque-to-hub segment on a separate reward ticket only if your hub connection has at least two hours of buffer, since ABQ's limited daily departures mean misconnects cascade badly on this itinerary.
January through March and again in October and November are consistently the softest months for fares on this corridor, as Luxembourg's business travel calendar (driven by EU institutions and finance) creates predictable troughs outside spring and early autumn conference season. Given how thinly scheduled this route is, setting up fare alerts specifically for the Albuquerque–Luxembourg pairing is the smartest way to catch the periodic Delta and Lufthansa business class dips before they disappear.