We leave in 2 weeks business class on Qatar for the first time, so just browsing Qatar's web site found this on their Lounges page
"For Privilege Club Gold members and first and business class passengers on any airline, the Oryx Lounge provides the perfect environment to work, relax, and freshen up."
It does not mention having to pay for access if flying business class with another airline so you may hopefully be OK. It would be tough to not have any lounge access included with a business class fare.