I have never participated in an L&L but it seems like you're basically working with:
- something easily digested over the course of a lunch break
- something that will help inspire discussion and interactive feedback
I think something like posing a question as to "how do you think we do X" and eventually revealing the current implementation would be interesting and thought-provoking for your listeners. You can abstract all the programming out of the equation so even non-coders could have a whack at it.
You could even abstract a complicated problem that your company faced as a riddle or puzzle. Like if you had to work with a square peg and round hole and eventually just chiseled down the square peg into a circular shape -- changing stock software to suit your company's needs.
I think any introduction that encourages technical thinking automatically opens up interesting conversation.
e.g. Time/Process optimization
How do you speed up your pie-serving waiter's operation? He serves a piece of pie and waits for the person to finish. He grabs their plate and takes it to the kitchen, then serves the next person. How can you satisfy your hungry customers more quickly if you don't care about dishes piling up?
I think simple metaphors to describe paradigms you use at work would be great food for thought while munching on a sandwich.