Lunches at our house are pretty relaxed and usually leftovers. Very often the conversation will go something like it did today.
Me: What do you want for lunch.
Me: Ok, get out the cheese. [Then offers choice of whatever fruit or veggie we have around]
GGirl: [Usually picks fruit]
Eat. Eat. Eat.
GGirl: Mom, I'm still hungry.
(Here's where the negotiations begin)
Me: What are you hungry for?
Me: Um, no. If you're still hungry you may have veggies.
Out comes the bin of veggie sticks. She either picks veggies or isn't really hungry.
She was recently introduced to Ants on a Log (aka: celery, peanut butter, and ants as she calls them). Today, that was the veggie of choice and she lined up the "ants" herself.
I find that if she makes the choices some of the time, there is less struggle when the choice is not hers to make. Works for me!