Personally my rule is you eat what is being served or you go without until the next schedule snack / meal time and hope you find that more palatable or you keep going without until you get hungry enough to be grateful that you have access to a wide variety of healthy food options ... I serve all the food at once including the 'fruit' portion cause I do not not want battles at meal time ... so if all they ate was the fruit from lunch that would be all they got that meal and no big deal for me ... they would not get 'seconds' of food until their plate was clean though because IMO if you are truly 'hungry' you will eat what you are served and IMO it is very disrespectful and ungracious to ask for more of something when there is still perfectly good food on your plate ... so if you eat everything and are still hungry that you can have as much seconds as available or 'healthy' as long as you have a balanced plate each time.... aka you can eat as much fruit / veggies / meat as you want but you are not having 5 helpings of just potatoes.
I would not be offering an alternative to have instead of the prepared lunch as IME this will open meal battles like the one you are currently having and it will snowball as more children see it 'works' for that child ~ children are smart and he can sense that the adults in his life are 'fearful' when he does not eat and he is using that as a strategy to get what he wants
Goes back to that question do we think that toddler children in Ethiopia and third world countries refuse to eat what is put in front of them? Do we imagine that they turn their nose up and say 'no I am not going to eat this maggoty rice this morning I am going to hold out for some yummy applesauce'? .... IMO we have picky eaters in North America because as adults we ALLOW picky eaters ... we are so concerned with some illogical fear that they will 'starve themselves' or 'go hungry' if they miss a meal that we cater and fold to normal 'autonomy' of children who are practicing with defiance to learn how they can control their world and turn meal time into a 'battle of wills' with the child ultimately winning even at their own peril cause it was never an issue about food or being hungry but rather the child trying to 'control' his environment .... unless a child has a true mental illness preventing them it is human instinct to EAT when hungry ..... it is one of our basic human needs and we will go through the garbage and eat bugs, slugs, rotten food or whatever presents it self if we truly are HUNGRY ... IMO children in North America are rarely truly 'hungry' because we have access to so much food .... now that is not to say they might be 'starving from malnutrition' but not because they are going HUNGRY but because they get served up crap that has no nutritional value cause it is 'cheap and child friendly' and we allow them a steady diet of this rather than forcing them to learn to palate healthy food instead
My understanding of human biology is an average human being can go 3 days without ANY food as long as they are drinking water to avoid dehydration before they have any adverse side effects health wise .... my guess even with our growing poverty is that there are few children in North America who go more than 1 day without eating something let along going the 3 days before doing any damage to their organs? IMO it is not going to harm a child to go without one meal cause he is refusing to eat it specially when we are trying to help them learn a life lesson that you 'need' a wide variety of food to be healthy and sometimes we have to eat foods we do not like in order to get that healthy variety .... if I only ate foods I truly LIKED my menu would very limited too like any child's and would consist mostly of Chocolate and Bailey's for nourishment