The more likely problem for Aer Lingus , as an EU based airline , is being able to operate a UK domestic route i.e . Belfast to Heathrow ,rather than a route between a UK point to anywhere in the EU.
Having said that the simple solution for IAG ,would be for BA to take over the
EI services on BHD/LHR.
EasyJet are securing the Austrian Aoc to allow them to operate intra EU ,not to secure the rights between UK and EU countries which I guess are assumed will be reciprocally allowed.