I have to agree with 411A - as this appears to be a new niche service for which Privat Air has the resources and Lufthansa does not. They make a profit where Lufthansa may make a loss, so using their own crew is not a problem.
In Europe we don't have all this fuss over scope, and this is in many ways a good thing, because routes that can never be profitable with the main airline CAN be profitable, make the main company money, and increase the network with a smaller subsidiary or partner.
Quite frankly it isn't taking Lufthansa jobs anyway as it is a new route, and why fuss about it when many of us have flown for subsidiaries in the past on the way up, or will fly for poeple such as Privat Air after retirement from the majors.
Good luck to Privat Air, a very well run and friendly company.