Another option, which hasn't been discussed, would be to open up the chat feature and ask if you could hop the line. The chat rep could liaise with the lounge staff. This is a way of quietly putting in your request (rather than drawing attention to yourself by walking up to the desk ahead of any line) and, if acceptable, the lounge staff could come escort you in so that it doesn't appear that you're demanding special treatment.

That said, I think the "special line", much like hotels or airlines, is the easiest way of sidestepping this issue given that it already works so well in those circumstances.