Katowice remains one of Europe's quieter arrival points for American travelers, which is precisely why the routing puzzle matters so much here. There is no nonstop option, so business class from Cleveland to Katowice inevitably means building a itinerary through a major hub, and the honest answer is that your two best bets are United via Chicago or Newark connecting onto Star Alliance partner LOT Polish Airlines, or Delta via a European gateway like Amsterdam or Paris working with its own metal or partners. United passengers get access to Polaris seating on the transatlantic long-haul segment—fully lie-flat, direct-aisle-access pods—before dropping onto LOT's shorter regional business cabin into Katowice, which is a recliner-style product rather than lie-flat given the short hop. Delta's approach typically routes through Amsterdam, JFK, or Paris-CDG, putting you in Delta One suites with sliding doors on the long-haul leg, again followed by a shorter connecting flight into KTW on a regional aircraft.
Having routed through both Chicago O'Hare and Newark on this itinerary repeatedly, my strong preference is Chicago when winter weather isn't a factor, since United's Polaris lounge there gives you a proper reset before the long haul, and connection times to LOT flights tend to be more generously buffered than the tighter Newark transfers. The insider move few travelers know: LOT's Warsaw hub, if your itinerary routes that way instead of directly connecting elsewhere, offers a surprisingly civilized business lounge and shorter security lines than Frankfurt or Amsterdam during peak mid-morning arrival banks, making it a smart choice if you have routing flexibility when booking.
January through March and again in October and November consistently produce the softest business class fares on this corridor, since Katowice's appeal is heavily tied to Poland's ski season in the Tatras and summer city-break travel, leaving shoulder months underpriced relative to demand. Given how few award seats and saver fares open on the LOT connecting segments, setting up automated fare alerts for this specific Cleveland–Katowice pairing is genuinely the smartest way to catch a release before it disappears.