Workdays are long and sometimes bleak, which is why it's nice to have office friends to eat lunch with. And if you're lucky, you will be immediately and organically enveloped into a warm and functional network of colleagues who invite you to grab burritos on Tuesday (or whatever).
Sometimes, though, you will realize that your place of employment has the culture of a joyless ice cave, and so you will have to initiate this process yourself. There is no shame in this; you are bearing the burden for us all.
Still, it can be daunting, this initiating. On the bright side, your prospects are exceedingly good. Already, you have one thing in common. (It is your job.) And so, if you are in the market for office lunch friends, or at least affable meal companions, consider this your pep talk.
I have generally worked in offices with eat-at-your-desk lunch cultures, and while this has obvious downsides, I would argue that it is actually an excellent setting in which to initiate lunch-based friendships.
That's because there is essentially zero risk! Asking someone if they would like to walk over to the new salad place to grab lunch and bring it back to eat alone at separate desks is about as low-stakes as it gets. In my experience, they will not say no, because people love leaving their offices under virtually all circumstances.
Grabbing takeout also has the benefit of being blissfully well-defined: you will leave the office for a finite amount of time, and then you will return. It's not "having lunch" — it's running a joint errand that happens to be social.
"Lunch" is an attitude, not a meal.
Depending on the culture of your office, lunch might not actually be your best bet for winning friends and influencing people. I have a friend who claims she has made all of her work friends through regular mid-morning coffee runs, which were already embedded into the office culture.
A possible lesson we can learn from this is that it is nice to work in a place with pleasant, pre-existing social customs, but a more useful lesson is that lunch is not the be-all and end-all of potential social interaction. If asking a prospective work friend to grab lunch feels awkward or overly ambitious, consider your alternatives. Hint: Usually, the alternative is coffee. That is fine. In this one instance, there is no need for creativity.
You don't actually have to go anywhere.
It is worth noting, too, that you can make friends without actually leaving the office, if you are short on time, or cash, or it is raining. I am a big advocate of asking prospective work friends if they want to literally go stand in the kitchen and "investigate the snack situation." This approach has been very successful! We don't even work together anymore and still, we sometimes "like" each other's pictures on Instagram.
If your office has no snack situation, "making coffee" or "walking to the vending machine to buy pretzels" work just as well. The point is to get up from your desk with another person and have a conversation.
Talk about something other than work (sometimes).
Speaking of conversation, yes, professional boundaries are important, and yes, some topics are likely best avoided while at the office, but once you've captured a potential lunch friend, it is worth getting to know them as a real human being with interests beyond "project management." This helps you avoid the trap of forging a friendship that is entirely based on complaining about other people in your office (a minefield). Additionally, learning about other people's lives is generally interesting, and probably makes you a better person.
Don't be afraid of being creepy.
Obviously, observe social cues. At the same time, don't let the ubiquitous fear of "being creepy" get in the way of reaching out to people you don't already know. A friend who works in academia says a former colleague struck up a friendship with her by literally bringing in extra food and then sharing it, and then it became a thing, and now they are best friends.
Should you do this? I don't know. The moral of this story is not that you should woo your friends-to-be with food (maybe?), but rather that there is nothing inherently creepy about enthusiasm.