Going to Europe, United and Lufthansa are in the same terminal at ORD, which would be an easy transfer. Same terminal building, no need to reclear security.

If ORD going AA to BA, you'll arrive T3 and depart T5. You'll need to leave security, take a tram and reclear security at Terminal 5.

On the return, both are a hassle. At ORD, all international arrivals are at Terminal 5. AA is at Terminal 3, UA is at Terminal 1. After clearing customs/immigration at T5, you need to take a tram to T3 or T1.

At JFK, if going BA to AA, you'll arrive at T7 and depart T8. After clearing FIS, you'll take AirTrain (the Jamaica/Howard Beach train) one stop to T8 and reclear security for AA. If going LH to UA, you'll arrive at T1 and depart T7 (same train, 4th stop).

On the way out, UA/LH via ORD is the easiest. On the return, it's a slight hassle either way.