No, Jackson Municipal Airport (MJQ) does not have a lounge, and the reason is straightforward: this small field in Jackson, Minnesota, handles general aviation traffic rather than a scheduled airline route network, so there has never been a commercial passenger base to support one. If you searched jackson minnesota airport lounge expecting a card-network room or an airline club, the honest answer is that none exists here, and none is likely to appear while the airport's traffic stays general aviation rather than scheduled commercial service.
Jackson Municipal serves private pilots, agricultural flying, and local charter and training traffic typical of a rural Minnesota county airport, not the ticketed passengers a Priority Pass or airline-club lounge is built around. There is no terminal concourse in the sense a hub traveler would recognize, no security checkpoint queue to wait behind, and consequently no market for a paid or membership lounge. The airport's role is functional and local rather than a gateway for connecting itineraries. Rural airports of this size dot the upper Midwest, and Jackson Municipal is a fairly typical example of that pattern.
For travelers in this part of southwestern Minnesota who do want a real lounge experience, the practical answer is to route through Minneapolis-Saint Paul International Airport, roughly two hours northeast, where Delta operates Sky Club lounges as part of its major hub operations, alongside Priority Pass options in other terminals. That is the nearest place the lounge conversation actually applies.
If your travel plans involve Jackson Municipal at all, it is almost certainly for private, charter, or agricultural aviation rather than a scheduled ticket, so budget for a small-airport experience with no amenities beyond basic facilities. Weather during Minnesota's winter months can add further uncertainty to an already limited schedule. Arrangements change - verify current services directly with the airport or your operator before you fly, though the underlying reality here, a general-aviation field without scheduled commercial service, is unlikely to shift quickly.