Leipzig isn't a destination that rewards improvisation, and neither is the routing to get there in comfort. There is no nonstop option from New Mexico to Saxony, so business class from Albuquerque to Leipzig always involves at least one connection, typically routing through a major East Coast or Midwest hub before crossing the Atlantic into Frankfurt or Munich, then a short intra-Germany hop to LEJ. American, Delta, and United all serve this corridor with meaningfully different products: American's best bet is its Flagship Business with the reverse-herringbone seat out of hubs like Dallas or Charlotte via a transatlantic partner, Delta leans on its excellent Delta One suite (sliding door included) departing from Atlanta or Detroit, and United counters with Polaris seats out of Chicago or Newark, both offering direct-aisle access on widebody configurations. My personal preference over dozens of similar itineraries has been routing through Chicago on United — the O'Hare to Frankfurt Polaris product is consistently reliable, and the connection times to regional carriers into Leipzig tend to be more forgiving than what you'll find funneling through Atlanta in peak summer thunderstorm season.
The insider move most travelers miss: book the transatlantic long-haul segment in business class but treat the final Frankfurt–Leipzig or Munich–Leipzig leg as a formality — it's often on a regional jet with no premium cabin at all, so don't expect lounge access or a hard product upgrade on that last hop. Instead, use your Star Alliance, SkyTeam, or Oneworld status to access the Frankfurt or Munich business lounges before that final short flight, since that's where the real recovery happens after a transatlantic redeye. Also worth noting: Leipzig/Halle Airport is compact and cargo-heavy (it's a DHL hub), so immigration and baggage claim move quickly — a nice contrast to the chaos of Frankfurt's connections.
Seasonality matters enormously on this run. January, February, March, October, and November consistently produce the softest fares, as Leipzig's trade fair and Christmas market crowds haven't yet hit and Albuquerque's own shoulder-season lull suppresses leisure demand. Given how much these fares fluctuate week to week across three carriers and multiple routings, setting up automated fare alerts is the smartest way to catch a premium-cabin deal before it disappears.