EI arrivals for sure. We did DUB-ORD last summer and they let you into the main airside T5 area but direct you (pretty sure a couple of EI employees) to the first exit down to baggage claim. I think F9 and EI both use the gates at that end of the terminal for this exact reason.
If I had a 5 hour layover at ORD and no Polaris access or luggage to worry about, I'd take the blue line to Logan Sq or Wicker Park before I bothered with any lounge at ORD.
This thread has been fairly entertaining and gone off the rails a bit considering the OP seems to be a run of the mill European amazed that domestic F doesn't get you lounge access in the US (a common misunderstanding, to be sure).