It has got very little to do with the EU and Aer Lingus wasn't being bullied. IAG's lawyers are more than capable of dealing with any bureaucratic bullies, not that there are any.
This service is being launched on the back of newly signed UK -US Air Service Agreement. Had the UK remained in the EU, they could have done the same using the EU-US open skies agreements and without the hassle of creating a UK Subsidiary. As it is, they are struggling to work around this new UK-US agreement due to ownership rules; rules agreed between the UK and US without EU interference.
They have had to create a UK operating company but the reality is that in relation to this UK-US agreement, they are a third country operator as they are ultimately owned by a Spanish consortium. Given the distressed state of the UK industry and the mounting job losses, I am surprised the DfT is even considering sponsoring this box ticking shell company as an "Airline of a Party". If it really is necessary to create competition on these routes post TCX, there are several UK airlines available to to do this work.