In my experience, popular Disney restaurants like Chef Mickeys that are showing as fully booked in the app are in fact fully booked. We have seen MANY people turned away at the podiums of various restaurants after inquiring about walk-up availability. Most ADRs will open up the day before as people cancel before the cancellation fees kick in. However, you say late lunch, but what time exactly do you mean? Just want to be sure the issue is not that you are searching just for 3pm or something, because CM today, for example only accepts lunch reservations until 2:30.