I've done this, but it was several years ago. Can't see why it would have changed, though--the Lounge is a benefit of GC membership, not of being an Aer Lingus passenger.
You should be able to get into the Aer Lingus lounge with an Aer Lingus Business class boarding card (only Transatlantic these days) or an Aer Lingus GC card and a oneworld airline boarding card (any class) .. or a one world partner airline GC card equivalent and a oneworld boarding card (again any class)
e.g. if you have a British Airways Silver Card this allows you access to the Aer Lingus lounge with an Aer Lingus / BA / American Airlines etc. boarding card.
Some airlines do allow lounge access for their top tier frequent flyers without boarding cards - BA & Lufthansa do I know ... but it's not so common - Aer Lingus don't as far as I know.
As regards the Anna Livia lounge - I've never tried but my understanding from the ads is you just call in hand over your €20 and in you go - advance booking not required. (it's upstairs above the shopping "street" beside the BMI lounge) - You can't camp out there all day - you're only allowed in 3 hrs before your flight.