Since you say it isn't an open-bar lounge, I would not expect to be carded upon admission but I would expect the bartender to card you. I would NOT mess with a fake ID - not because I expect the bartender to be cross-checking with the front desk, but because of potential repercussions. If you get booted from a local bar, no big deal. A potential ban from Skyclubs or a call to the airport police would be much harsher IMO.
I'd probably have no qualms ordering the drink, but if asked for ID just change my order. "Oh, never mind then, my ID is over in my bag I'll just have a Coca-cola". They'll know what that means and everyone saves face.