Berkeley (JBK) is not a real scheduled commercial airport, so a search for a berkeley airport lounge is chasing something that does not exist rather than something the field simply lacks. The JBK identifier is historically associated with a small general-aviation field near the Berkeley Marina in the East Bay, used for small aircraft rather than airline service, and it has never operated the kind of passenger terminal a lounge would belong in.
For anyone actually flying to or from the Berkeley area, the real airports are Oakland International (OAK) and San Francisco International (SFO), both a short drive away across the East Bay and the Bay itself. These are the fields with genuine scheduled airline service, and any lounge research for a Berkeley-area trip should be pointed at one of those two rather than at the small general-aviation strip the JBK code is tied to.
Oakland International carries a modest but real lounge picture for its scale, including airline and Priority Pass style options tied to status, premium tickets, or a qualifying card, useful for East Bay travelers who want to avoid the bigger crowds across the water. San Francisco International is the larger hub of the two, with a wider spread of airline clubs and third-party lounges reflecting its size as one of the West Coast's major gateways.
If your itinerary says Berkeley, the practical move is to identify which real airport, Oakland or San Francisco, you are actually flying from, and research lounge access there rather than at a small-craft field with no passenger terminal. Confirm your booking's actual departure airport before you plan around any lounge, card benefit, or day pass, since the Berkeley name alone will not point you to the right facility on either side of San Francisco Bay, and airline apps list the real airport code, not JBK.