Katowice remains one of the more delightfully obscure endpoints in premium travel, and there is no nonstop path from the Nevada desert to Poland's industrial-cultural heart—so the real craft here lies in the connection. Business class from Las Vegas to Katowice invariably routes through a major European or American gateway, with Delta's transatlantic joint-venture partnerships and LOT Polish Airlines' Warsaw hub forming the two most sensible spines; United, meanwhile, offers its own Star Alliance routing that can dovetail nicely with LOT's onward Katowice service. Total journey time typically lands around 11.5 hours of pure air time, though realistically you should budget closer to 14-16 hours door-to-door once you factor in the connection.
Having routed this itinerary through both Amsterdam and Warsaw on separate occasions, I'd steer discerning travelers toward the LOT connection whenever schedules allow—flying Delta's Delta One suites (with closing doors on the 767 and A330/A350 fleet) from Las Vegas to a European hub, then transferring onto LOT's Warsaw-Katowice hop, gives you lie-flat comfort on the long haul without wasting a premium seat on a short regional sector. United's Polaris seats, particularly on the 777 and 787 fleet with proper suite doors, are a strong alternative if your LAS schedule favors a Chicago or Newark departure. The insider move: book the LOT domestic Warsaw-Katowice leg as a separate short hop when award availability on the connecting partner segment is scarce—LOT often opens up saver seats on this regional leg even when the transatlantic space is locked, and Warsaw Chopin's compact layout makes tight connections far more manageable than sprawling hubs like Frankfurt or Heathrow.
January through March and again in October and November are your sweet spots for this routing, both for fare softness and for avoiding the summer crush of Polish diaspora travel that clogs LOT's transatlantic partner flights. Given how thin and volatile premium inventory can be on a route this niche, setting up automated fare alerts is genuinely the smartest way to catch a fleeting release of business class space before it vanishes.