Ya know the only things on your list that are low carb is the chicken and lettuce? Fussy eater or not, you may have a tough time doing low carb if you won't eat or try anything but what you listed.

Other choices would be:
brocolli, cauliflower, green beans, zucchini, squash, tomatoes, mushrooms, radish, cucumbers, eggplant, asparagus

beef, pork, lamb, fish, shellfish, veal

eggs

cheese

olive oil, butter

fresh or dried herbs

The stuff you listed isn't exactly what I would term a healthy diet. More of a high starch one.