OK, someone else will be along shortly to confirm (or not) but IIRC there is a Oneworld rule about Lounge access on a trip that contains a long haul as well as a connecting short haul, even where one of the flights is in business and the other is in economy. However that applies to Oneworld airlines and technically EI is not a member (though rumours abound about it joining). So I think you are still out of luck unless you are an amazing sweet talker and can blag your way in!