Getting to Timisoara in a lie-flat seat from Indianapolis requires patience and smart routing, since no carrier offers anything close to nonstop on this city pair. There is no true business class from Indianapolis to Timisoara without at least one connection, and typically two: IND passengers generally route through a major East Coast or Midwest gateway before crossing the Atlantic via Frankfurt, Munich, or Istanbul, then dropping south to Timisoara on a regional jet. Lufthansa's Frankfurt and Munich hubs are the most dependable option, with mainline widebodies offering their long-haul business class seat on the transatlantic leg before a short intra-European hop completes the journey; travelers lucky enough to catch Lufthansa's newer Allegris cabin on select routes will notice the difference immediately in privacy and seat design. Turkish Airlines via Istanbul is the other serious contender, and I've found their business class product — with the signature bar/lounge area on widebody aircraft — genuinely competitive for this itinerary, especially since Istanbul's connections into Timisoara are frequent and well-timed. TAROM, Romania's flag carrier, typically handles the final domestic-feeling leg into Timisoara and occasionally codeshares on the longer segments.
Having routed through Munich and Istanbul multiple times myself, my strongest recommendation is to build in a deliberate long layover — three to four hours minimum — in whichever European hub you choose, since Timisoara connections are limited and misconnections here mean a full day lost rather than a quick rebooking. Istanbul Airport's lounge, in particular, rewards travelers who linger rather than rush. Winter months tend to see softer demand into Eastern Europe generally, which works in your favor.
Given the complexity of routing and the lack of a dominant carrier on this corridor, fares fluctuate more than on typical transatlantic trunk routes, so setting up automated fare alerts for Indianapolis to Timisoara business class is genuinely the smartest move — the sweet spots in January, February, March, October, and November tend to appear and disappear quickly, and a tracking tool will catch what manual searching often misses.