Aerlingus said before that their new base outside of Ireland would connect that base to other European cities. In that respect I think a Heathrow base is a crap idea.
Most of the European cities that are on Aerlingus's routemap already have a Heathrow service. And those that don't have some form of London service.
I prefer the idea of Aer Lingus setting up a base somewhere and mainly introducing non-existing routes. Only setting up a base to compete with carriers on existing routes isn't very profitable (particularly in the short term).
Anyway, this LHR base story is totally not creditable, and not backed up by any evidence.