Continue to pack her only veggies; if you can cook only vegetarian at home for a week or so, with varied veggies. She definitely can't go hungry for a whole week.

Then don't put her vegetables, she doesn't has to eat them if the doesn't like them. I hated vegetables since i was a kid(because of their forms, colour and odor) and i grew kinda healthy (22 y.o, 188cm/6'2" approx, 80kg)

I would have beat my kids ass. lying could have gotten you in serious trouble and may if she keeps doing it. I would be making only veggie dinners until she got over it. I understand not liking a certain veggie, but this lying about not getting fed is crap.

Does candy corn count?

Maybe try working together with your daughter to figure out what she doesn't like about vegetables, the taste the texture, how they're prepared etc. Are you just tossing raw veggies in her lunch? Maybe try being more imaginative than veggies + dip. Have you tried different methods of cooking them? Kid I babysit liked raw bell peppers but then started to not like them, but when I roasted them he loved them again.

So if you have a picky eater, maybe try changing how you present the vegetables. If they're always cooked, try some raw ones. If they're always raw, try some roast veggies. Seasoning things always helps--dips, spices, olive oil, it all works. No one likes everything. Let your kid try new things. And stay away from greens unless they're raw and in a salad--your kid is probably still young enough for bitter flavors to come through too strongly.