It shouldn't be difficult to adapt GPS-based dating apps (a la Growlr) for something like this. It can target lounges by any airline at any airport.

Travelers who wish to be invited - they can pay for the app at download, or per use. Can give a brief description of themselves, preferably with a facepic too. Elites / premium pax who wish to invite others - similarly could pay per listing, and can also set a price for each invite that can be transacted outside of the app.

Especially since I don't think inviting strangers (even for a fee) to a lounge is against the rules, I am surprised nothing like this has been put together yet.

In the absence of such an app, for me personally, I do try to look around the entrance area to see if I can spot someone (cute) who wish to be invited when I am lucky to be flying near the front. It's just good karma for when I am not.