Hello.

As someone mentioned, yes they can use the United lounge if they are flying a different airline. Logistically, I don't know if it is possible or worth the effort. Aer Lingus operates from the International terminal E and United operates from terminal C and A at Logan.

I don't know if the TSA will let you through security at terminal C or A with an EI boarding pass. Even if they do, you'll need to leave the lounge early enough to get to terminal E to clear security there.