Usually when you are trapped in all day meetings, the easiest thing to do is to just ask, "Can we take a lunch break now?" If you have a medical condition that means you can't miss meals, then you could bring that up as well particularly if they seems disinclined to give you a break. If you have a medical condition, then by all means, plan ahead and bring something with you to the meeting.
However, you need to time the questions for most effectiveness. If the Directors are only there for an hour or so, then wait until they are gone. It could be that the normal lunch time is the only time they are available and that is why they are showing up then.
I also try to wait until there is a lull in the discussion or right as we finish one topic and get ready to start the next. When you do it as you change subjects, you can say something like, "I think we might all be able to cover XYZ better (or more effectively or faster even) if we break for lunch first."
I have often found that everyone wants to take the lunch break, but no one wants to be the person who brings up the subject.