Hi there.
planning a trip in business next year , from Dub- Mia and return
it’s my other half’s first time in J so wanted a nice experience.
originally my plan was to fly EI from Dub -JFK to take advantage of pre-clearance and then AA first to Miami
however after advice it now seems that Dub-LHR -MIA
with AA would be better to enjoy the T3 lounges .
on return , would people suggest BA on A380 Club World , or Iberia business via MAD ???

It depends what you value/enjoy most.
Personally I would choose the EI+AA option, I like the pre-clearance and arriving in the US as a domestic flight is a pleasure. At DUB you have the "51st&Green" lounge which is pleasant but not spectacular; one step below the standard BA lounges at LHR T5 and few steps below the choice you have at LHR T3.

The option DUB-LHR-MIA to enjoy the T3 lounges is possible but make sure to book a connection with a substantial layover at LHR as you will have to change terminal from T2 to T3 if flying EI or T5 to T3 if flying BA. You will get a much more pleasant multiple Lounge experience but a more stressful connection at LHR and a less pleasant arrival in the US.

I'd return on IB via MAD. It is a good airport and Iberia Lounges are good.

If you want a full lounge experience, go via LHR T3 and come back via MAD, making sure to leave an extended layover. You'll experience a variety of good lounges

Everyone will have their own preference for lounges, but I would personally not go via LHR for T3 lounges, especially business lounges (you don't have a status in your profile so assume you don't have OW Emerald to get into the F lounges).

I'd also likely go the IB route back via MAD to avoid LHR. It's a slightly longer flight in euro-biz but I don't love LHR either. Having said that my last EI flight to LHR actually used the TATL config A321 with a proper business cabin, I don't know if that's the norm, but was a surprise.