My DD is 2. I have to say THE best thing we did for her eating (although she isn't particularly picky) was to all sit at the table together. We have done this for... more than a year, and she eats so well.
Here are our lunch ideas.
Muffin, or square bread pizzas (ketchup, cheese and any topping you like. ham, pineapple, sweetcorn, tuna, mushrooms etc etc)
mini quiche
soup
Leftover chicken goujons and dip
tortilla wraps
scrambled egg on toast (ketchup really helps)
Hummus, or houmous and breadsticks and/or veg/ salad
Bean salad.
Sandwiches/crackers/bagels
cheese
ham
tuna
grated cheese, grated carrot and mayo
Marmite and cheese spread
egg mayo
sausages
banana
peanut butter
avocado and cheese spread.