I was in your shoes just a few months ago! The worker may or may not partake, but especially since it is around lunch time, I would have some snacks available...cheese and crackers or nuts would be some of the things I would think about for the protein at that hour. If it were me, I would also make sure to eat something shortly before the worker arrived...in case the worker does not eat and you don't feel comfortable eating without him/her.
I am sure it will be fine...that's what everyone told me when I was so nervous, and it was. In my case, I offered my worker something the first 2 visits and she refused both times so I did not offer the 3rd time. I have heard of workers, accepting, though and am glad I offered.