For OW lounge access based on status, you must be flying on any OW flight in any cabin departing from the airport in which the lounge is located. You will get lounge access based on your status, -- Emerald gets F lounges, etc.

One notable exception to this is lounge access for AAdvantage members flying domestically. I believe that they must be members of the Admirals Club for admission except certain nonstop transcon pax who get FL access if ticketed in the F cabin. Or something like that.