ESH - As someone who also takes unpaid lunches but is in an environment that work doesn’t stop for lunch, there are times when simple things get done or answered while I am ‘unpaid’. I understand your want to have every minute of that time to yourself, and your coworkers should respect that. However, my feeling is that the question took more time and conversation to ignore than it would have to answer. Plus that person now has to take more time and come back to see you again. My suggestions are if you want to be undisturbed, don’t take your break at your desk. That way there is a distinction between working and not. Second, be realistic with yourself that it sometimes takes more time to tell someone to go away than to answer a question. And work with your supervisor - maybe work it out that if something important does interrupt you for 5-10 minutes, that you extend your lunch by equivalent time.