It is odd that she would do that, but eh… people. Whatcha gonna do?
Maybe she chose a restaurant that she thought you would like.
If anyone cares for an update…
I sent an email to the friend thanking her for her company at lunch and suggested that next time we get together we should gather a few friends and try to do a potluck. She teased me a little about the fact that I would probably just end up buying whatever I was slated to bring (totally true) and that she was up for it, but really enjoys the dining out experience because she doesn’t get to do it as often anymore.
That doesn’t really answer my question about why she brought her own food, but at least it gives me an inkling that it’s some combination of a diet restriction and that she likes sit-down restaurants.
Ask her! Directly! As in; “Before we make another lunch date can you share why you brought your own food into the restaurant?”
It may turn out they’re all trying to accommodate you, who ALWAYS eat out!
Only one way to find out. Ask her!
It’s weird.
It’s weird, especially if she didn’t know that it was weird and at least try to explain it to you.
I work on a college campus, and there’s a museum cafe next to my building. Lots of people meet there to talk, etc., and once I absentmindedly started eating a sandwich I got from a food truck. Chef was over there in a second to ask me to leave (or stay and not eat).
A place where you’re seated by a waitperson is absolutely a place you cannot bring your own food. It’s rude, it’s tacky, and frankly, exploiting the restaurant. You can eat in a park or cafeteria at work if you want to go this route.
By coincidence, something similar just happened to me. I met a friend from Kazakstan at a coffee shop here in Jakarta. She had taken part in a Kazakstan cultural exhibit earlier in the day. To my discomfort, after we had ordered beverages she pulled out a styrofoam container of food from the exhibit and wanted me to try it.
Talk about a cultural mash-up…I really don’t know what the Indonesian take on this would be. I did not want to be rude to my friend, because I don’t know her very well, I didn’t want to hurt her feelings, and I have no idea how she’d take it through her own cultural lens.
In the event, the nice servers brought us plates, napkins and cutlery (which we did not ask for, of course) even though we only ordered drinks, not food. I thanked them profusely.
The whole thing was a bit embarrassing. I’m glad it’s over now. The halvah (who knew that was a Kazakstan food? I sure didn’t) was lovely, I will say that.
It does seem a little weird, but as others have pointed out there are myriad plausible explanations for her behavior.
The only way to know for sure is… Ask her. 
Don’t jump to any conclusions. Wait until PSXer comes and shares his opinion. Should be a good one.
I think this is very weird but then here in Massachusetts it would be illegal to bring outside food into a restaurant (I think some allowances are made for babies). If this was a one time thing then let it go but if you’re going to get together for a meal again you should bring it up. People upthread have suggested how you might phrase it, but you have to be willing to do it. Ignoring it and letting this go on is unfair to you (because you’re obviously distressed) and to her (because you’re resenting her behavior).
When I worked in restaurants, I saw people bring in things like apple slices and Cheerios for a toddler, or their own salad dressing. I’m OK with that. But bringing in food from another restaurant? C’mon, just stay at the first restaurant and eat it there.