I don't think this is easily possible. If nothing else, it's complicated as by the time you're in the lounge, immigration wise you're then in France...

Best bet is to speak to the Eurostar staff when you get to St Pancras. In the past, I've left tickets for late arriving friends at one of the manned checkin station / booth things, and texted them which one it was. Said friend then skipped the automatic checkin gates, went to the booth, showed some ID, was manually checked in and handed the ticket.