Surely she is not choosing her lunch if she is having to choose a veggie option in order not to get teased by her friend, though, Acanthus?
It's not the fact that she is eating the veggie option that's the problem, but the fact that she is feeling coerced into a particular 'choice' by her friend. That is not a good thing for a friend to be doing, nor is it fair for the Op's dd to feel she can't have what she wants for her lunch, for fear of what her friend will say.
I agree with SPB that the best thing to do is to tell the girl that she doesn't have to listen to what her friend says, and to equip her with some facts and some come-backs to use when her friend starts to have a go at her for choosing a non-veggie option.
"It's my choice what I have for my lunch, and you should stop bullying me about it."
"I don't tease you about your choice of food and you shouldn't tease me."
"Friends don't tease eachother, and you are making me unhappy."
In my opinion, this is getting very close to being bullying - it is not a one-off incident, and it keeps on happening, and I see no reason why the OP should relax and let another child carry on doing this to her child.
I would be appalled if any of my dses were forcing their views onto another child like this - and this girl's mother should be focussing on the unpleasant behaviour of her child, not condoning it because it chimes with her views on food. Does she want her dd to grow up thinking it is OK to tease/bully/coerce others into doing what she wants them to do??