Viper,
Use your head man

This is what you do. You two site beside eachother right? And I assume you work days (i.e. you'll have the same lunch period or dinner period if you work evenings?). OK, now follow these easy steps:
Step 1) Pop your head over the cubicle wall and say "Hi, umm I know this sounds stupid, but I'm really craving Greek/Chinese/Pizza/fill in you choice of food here, but I'm short a couple of bucks. I was wondering if you wanted to pitch in literally two bucks for some food and when it comes I'll give you half.
Now, she can either say 1) "Sorry I brought lunch" 2) "I'm not really into Greek/Chinese/Pizza/etc or 3) some other variant of the word "no", or...if she's really smart she could say 4) "why don't you just use a credit card?"
You can turn response number 1 and 2 around. For number 1, just say "hmm...OK. You sure you really want to eat your bagged lunch? I heard the Greek/Chinese/Pizza place is really good...you can always eat it later." For number 2, just say "well, we can always get something else...I'm just really starved" and for number 3, just accept no and say "alright, thanx anyways...by the way, my name is <insert your name here>" and offer your hand for a nice handshake.
If she says number 4, take note of her quick thinking and say "I would, but I left half the contents of my wallet at home...that explains my lack of money...just have whatever small bills and change was in my pocket."
Step 2) If she says yes, get her two bucks (you won't need it...bring small change like 5 dollar bills so that it really looks like you're short). Order up the food, and when it comes say "You know what...why don't we go eat someplace else". Now find a good place to eat, and go with her to have some lunch. If you've gotten to this point, there's no way she'll eat someplace else.
Anyway, my point is, you don't even have to follow my suggestion, just come up with something creative like this. At worst, you've formally introduced and broken the ice so you can pop your head over the cubicle later. At best, you've met, you've had lunch and you can size up her personality and earn some brownie points. Have some fun man...flirting is so much fun and it doesn't have to even amount to anything and it'll still be fun.
-GL