MAKE IT FUN!! Let him pick out something new at the grocery store every week or every other week.....PREFERABLY from the produce section. Make it an EDUCATIONAL process......how it grows, where it grows, what good nutrients does it have, etc? The MORE you understand WHY, the more apt you are to do, try, etc.
How about wraps instead of a sandwich? String cheese wrapped w/ a slice of turkey and whatever condiments he wants....boiled eggs, nuts, most all fruits, avacado.
Set some "house rules" for eating. We have a "courtesty bite" rule. If someone took the time to prepare, you at LEAST need to show them the courtesy and respect to try it. In addition, you need to remind them that it may become their new "favorite thing." When they hesitate, I ask them if they like kiwi (or something I know they like). When they respond, "YES", then I ask how they know.
Of course, they tell me they tried it. POINT MADE. We even "suggest" a three bite rule before you make a decision. I ALWAYS tell them I appreciate their effort and willingness to try it, even if they decide they don't like it.
Start letting HIM make some food choices at the store AND in meal prep. When choosing which vegetable.......ask him....peas or green beans......apple or kiwi, etc.
I've taught nutrition for DECADES and know that the earlier you TEACH them, the healthier they'll be AND the better prepared they are to make good food choices. Food choices are something you must make EVERY day of your life, so it's something that needs to be TAUGHT.
BTW.......Lunchables are one of the top 10 WORST foods according to the Nutrition Action Newsletter.
Sounds like this might be an EXCELLENT time for you to learn some things TOGETHER! I ALWAYS tell the kids, "It's FUN to learn & try new things".