Aer Lingus already has relationships with the oneworld members that it makes sense for them to deal with. They codeshare with BA & AA and interline with AS. There is a limited degree of FFP earn/burn potential between these. Furthermore, you can apparently spend your AerClub Avios on IB flights from within AerClub (not that I have looked to much into that); in any case, you can move your Avios to any of a BA, IB, QR, AY, VY account and book on those, too.

Of course, EI still has (limited) partnerships with UA, AC and B6.

What oneworld carriers are left over?

• CX Cathay Pacific - neither airline serves the other's hub (though there is "overlap" at AMS, CDG, FRA, LHR, etc). Not an obvious/natural partner
• JL Japan Airlines - neither airline serves the other's hub. Not an obvious/natural partner
• MH Malaysia Airlines - neither airline serves the other's hub. Not an obvious/natural partner
• QF Qantas - neither airline serves the other's hub(s). Not an obvious/natural partner
• AT Royal Air Maroc - neither airline serves the other's hub. Not an obvious/natural partner
• RJ Royal Jordanian - neither airline serves the other's hub. Not an obvious/natural partner
• UL Sri Lankan - neither airline serves the other's hub. Not an obvious/natural partner

The same can be said about FJ - Fiji Airways and WY - Oman Air.

Aer Lingus' partnerships with AA, UA, B6 and AS cover most of North America; for the rest of the world, it's got BA. It's part of the oneworld TATL immunised Joint Venture. It's got as much of the world covered as it probably needs to. It doesn't gain anything from voluntarily submitting to full participation in oneworld.
It's got all the "alliance" benefits it requires, so I genuinely don't see why Aer Lingus would go to the bother and expense of preparing itself for oneworld membership, when it already has all of the markets in which it is interested fully covered by the existing network/patchwork of agreements.

Believe me, I'd love if Aer Lingus was a full oneworld member, but at least these days, with earning finally "switched on" for BA flights, AerClub members are already in a better place than they were for the first 10 years of IAG's ownership.