We're a vegan family and I wouldn't have any problem with that. We're already dairy and egg free and our play group is nut free, so it's not a big deviation from normal for us. Some of our non- baked lunchbox snacks are:
Veggie sticks and hommus/pumpkin dip/babaganoush
Baked beans
Roasted sweet potato or pumpkin cubes
Sugar snap peas
Cucumber rounds
Bliss balls (we use sunflower seed and oats)
Coconut yoghurt (home made but if this is too hard, make coconut custard with custard powder, or buy some)
Bread sticks (spiced baked sandwich crusts)

For sticking together a sandwich there are heaps of options. We use Nuttelex, if we're having vegemite, otherwise not. Hommus, sunflower butter, almost any Vegie purée, and lots of bean based dips. I make it up as i go along! They freeze well.