How would you play that out with passport control also.. Then customs to come back in again, I'm confused?
Not sure if I would play around like that in TLV
I assume that there is some security pass to get through, like in JFK with UA (?)
how on earth would amex concierge be able to help you? you dont want refundable tickets, neither to fly, just a visit to an airport gate/terminal? hey and buy me some duty free stuff to whilst your at it, not gonna work
and the Dan lounge would be more of a dissapointment than a suprise.
Amex could have tried to look into it. I do not know. What do you want me to buy you in duty free?

(flying in a week) I've been to the lounge so I know what you mean, depends on what time. I thought it would be nice to walk around. If no one here has info how to get in and I find out, I'll try to update. I was there today but did not have time. I think it is possible.