I booked a business class ticket on Swiss ORD-ZRH (I booked with United miles if that matters). I have a 6 hours layover in Zurich, followed by a ZRH-DME flight that I booked separately in economy (I paid cash for this leg and it's a completely separate reservation).

Is it possible to access the Swiss lounge in Zurich on arrival for my 6 hour layover? Or will that not be possible since my second leg is economy?

Thanks