yes, so that's a slightly different allowance, and there is no requirement for you to be on a BA codeshare of an EI operated flight and on a BA ticket. as long as you are on an EI flight then as a gold or silver you can use the EI lounge in T2.

for the reverse at DUB there would be lounge access if on a flight to LHR, but note that it wouldn't apply if you were on a Aer Lingus Regional flight so that would put most of the EI flights to the regions out of scope. so for example if i was on a EI regional flight to LBA I wouldn't get access to the EI lounge at DUB, but if I was on a EI mainline flight to LHR I would.