Does Aer Lingus release business class award seats to Qantas?

I am wishing to fly from Dublin (Ireland) to Los Angeles, business class, using Qantas Reward points. It is fairly easy to find reward seats with British Airways, but that involves flying via London, taking 3 hours longer and involving two flights, not one. Aer Lingus offers a direct flight, but I have only found Economy seats. Does anyone know if Aer Lingus Business class is ever offered? I am only a Silver status Qantas member, btw.

Hi,

This page below seems to suggest award space for business class seem to be harder to come by.