ds (16 months) won't eat sandwiches either. It is a real pain particularly when we go out. I usually give ds a cooked lunch. I do a lot of batch cooking and freeze in small portions so I just usually get something out of the freezer.
I might cook a load of bolognese sauce and freeeze portions that way you just need to cook the pasta, defrost the sauce add cheese and you have lunch. Other things I cook and freeze are
cauliflower cheese
shepherds pie
spinache lasagne
Risotto
Fishpie
Easy things to make on the day - not out of the freezer
Omelette
Jacket potato with tuna mayonnaise(just use the microwave for the potato) with cooked veg (usually frozen veg)
potato (again cooked in microwave) with salmon (again just cooked in microwave for a couple or minutes with some butter melted on)
Cous cous (you just ad boiling water to the cous cous and let it stand for 5 mins and it is cooked - really easy - you can add some cooked frozen veg too) with meatballs and tomato sauce
The meatballs are easy (minced meat with chopped up onion and garlic, 1tsp of cinamon or herbs and some tomato paste - mix together and roll into small little balls) you just grill them for 10 minutes each side - mix with a tomato sauce (out of freezer) and serve with cous cous and vegetables. If you make more than he needs You can freeze them after grilling them and then get them out and heat them through in the microwave next time (defrost first)
Pesto pasta - whizz up fresh basil 1/2 clove of garlic and pine nuts in the food processor and add some olive oil until you get a paste. then add some parmesan cheese - This keeps in the frige for a week and you can add it to pasta.
Pasta does tend to be a staple quick meal in our house.
Also you could try a more finger food type lunch though ds doesn't like these much either
eg avocado, rice cakes, cheese bits, tomatoes and serve with some houmous or cheesy dips.
Also I occasionally give ds a jar if I'm really rushed.