Would he possibly eat a lunch packed by mom - what if mom and boy got matching lunch boxes and she made both lunches and then when it was lunchtime - possibly ask him to come and eat his lunch while you are cooking so he is alone. Tell him that that is the time that mommy will be eating out of her lunchbox at work - whether it is or not. Then let him pick at whatever is in the box and make no comment. When you serve lunch to everyone else ask him if he would like some but dont' force it.
He might enjoy being able to send mom an email after lunch and tell her something about the meal like what he liked the best about what she put in his lunchbox or about a snack or meal you made that he ate some of.
I would try to keep a sippy bottle of water where he can get it anytime he wants so he stays hydrated.