Omega Airport (OMG) in Namibia's Zambezi Region has no lounge, and the more accurate way to frame the question is that it has no scheduled airline service at all, so there is no passenger network for a lounge to serve in the first place. The airstrip sits at Omega, a settlement that grew out of a former military base in the Caprivi Strip and now serves the surrounding community, with air access limited to charter, government, and aid-organisation flights rather than any commercial route.
That absence of scheduled service is the real reason a lounge does not exist at Omega, rather than any simple lack of terminal building. Charter operators and occasional government or aid-organisation aircraft use the strip on an as-needed basis, without published timetables, ticket counters, or the passenger volume that would ever justify a waiting lounge. Travellers reaching Omega typically arrange transport directly with the operator flying them in, and there is no public terminal process to speak of beyond a basic airstrip and access track.
For an actual lounge, look toward Namibia's real aviation network well beyond Omega. Katima Mulilo's Mpacha Airport, the regional hub for the Zambezi Region, has scheduled domestic flights but no lounge of its own either, being a modest regional field. Windhoek's Hosea Kutako International Airport is the country's genuine international gateway, connected to Katima Mulilo by FlyNamibia's domestic network, and it is at Windhoek, not at a remote regional strip, where anything like a business or premium lounge would realistically be found.
If your travel involves Omega, treat it purely as a point of arrival or departure by charter, arrange your ground transport in advance, and reserve any lounge-network membership for Windhoek or an international connection elsewhere on your itinerary. The Zambezi Region's rainy season, roughly November to April, can also bring seasonal flooding that affects unpaved airstrips like this one, so confirm timing directly with your operator.