Allright, here it goes for Athens:

Is there any immigration/security fast lane:
YES

Inbound:
Not sure. The only flight this would apply to is the RO flight(s), as they are not in Shengen. Delta stopped their ATH service afaik. For Shengen flights there is no need (No control).

Outbound:
Yes there is. Loyalty card won't help you at the security checkpoint though, the correct procedure is to get a lounge invitation at check-in, and have your boarding pass stamped for fast-track access at the lounge.