I have never really seen them available. They pretty much always get quickly booked.
While there are no guarantees of getting a room close to the lounge, given the mobility challenges, WDW is usually pretty good. If not DVC, the room will almost certainly not be on the same floor as the lounge, but may well be a short walk to the lounge via elevator.
If you are CL, you are also allowed to bring food/beverages to the room. Generally speaking, if you end up bringing food to the room, getting it from the lounge is easier than going to the quick serve. Even at AKL, it is usually closer to your room, and the food is self-serve, so there's no line, and no waiting for a CM to get your order.
The only catch is that the CL's don't have trays or dinner plates. I'm not 100% sure what AKL has these days though, as my most recent CL stay there was some years ago. In all seriousness, in your situation you might be able to call the hotel ahead and see if they can provide a tray, or consider bringing one if you book CL. In some cases, the CL staff might be willing to help in other ways too, if you explain your situation.