Even as an AA PLT or EXP, I don't think there would be access to an AA lounge flying on a non-OW carrier (with the possible exception of codeshares that somehow involved an AA flight number...).

With the exception of BA Gold / opendoors access, the key factor becomes that the OP is flying Icelandair. None of the alliance access rules are going to apply to a passenger flying Icelandair, because Icelandair isn't partners with any of them!