I've been through Antigua several times in the last few years (although I add the health warning that it's been 18 months since I was last there - someone else might well be along shortly with more up to date inforrmation).
The third-party lounge is landside, up the stairs by the entrance to departures. It's a pretty standard Caribbean lounge and certainly nothing special: ok for a quick beer and some crisps for a short time, but I wouldn't go out of my way to visit it.
In the past, and assuming you'll have more than half an hour or so to kill, I'd have recommended heading over the road to the Sticky Wicket, which was a much nicer way of killing time than the lounge (albeit you had to pay for food and drinks). The Sticky Wicket was affected by the collapse of the Stanford Group and I'm not sure if it's still open, but worth checking.
David