I would not think that you could discipline an employee who was outside of the premises walking to a shop or something, in their lunch time.Unless of course they are wearing the establishment uniform and this can been seen clearly.
Even then I don't know.
Have seen for example people in uniform , say nurses ,or bank staff doing shopping in supermarkets or having a1/2 lager in a pub, in the dinner hour, or a fag in the street as they walk along.. But I don't know if they are on duty or not, or if their duty is finished.
So sorry not really able to help.