Is this normal behavior at a group lunch?

Her actions give the impression, that for some reason she got upset and didn't want to be around the rest of you.
And yes, her actions were rude.

If she wasn't upset, the polite thing to do would be to stay and wait for everyone to finish eating.
If she really just wanted to walk out, she should have excused herself politely. e.g. "Please excuse me: I'm going outside."

Maybe she needed to poop.

I think each and every person in the scenario is overreacting. You all just need to let it go and move on.

I just don't care.

Sounds like a cunt. Also, this is some pathetic High School melodrama bullshit, what the fuck is a grown as woman doing acting like a teenage bitch!?

I'd bet money that she has a panic disorder she's ashamed to admit to having. As someone who has dealt with panic attacks for a couple of decades, I can understand that "I need to get out of here Right. Now!" impulse that undoubtedly feels utterly crazy to anyone witnessing it without an understanding of the compulsion that motivated it.

If she were open about what was going on in her head (assuming she has a panic disorder), she was probably worried that she was going to be ill, have a heart attack, or suffer some other fate that feels overwhelming and catastrophic at the time. It's an unreasonable disorder; you can't just jolly yourself out of a panic attack, and although you can minimize them, making them disappear isn't always possible. Some people find the condition humiliating and frightening in the extreme and never seek help for it, which is a shame.

Yes, she should have explained. As embarrassing as it is to admit that I still have panic attacks that occasionally bring on some weird actions, I feel I owe it to others to say, "I'm sorry, I have anxiety attacks sometimes, and I'm going to grab some fresh air." I'd rather deal with a little personal indignity than make others feel as though they had done something wrong.

In your friend's case, being repeatedly asked about what happened and why she left may not be a question she could answer if she's still dealing with the shame of being what some people consider "crazy" (it isn't crazy, but it can feel like it is to people suffering with panic disorders). She probably became indignant to hide that shame. Does she stay home a lot or prefer to go to familiar places? Does she prefer to drive? Does she make frequent trips to the bathroom? Those aren't proof of a panic disorder, but they're often signs of one. Familiarity and a sense of control are common ways people deal with panic.

Another possibility is that she really needed to fart, which invokes shame of a different sort.

TL DR.

I read this when it was first posted, and have been thinking about it ever since.

Have you ever been in a situation you don't want to be in, and just fantasised about simply getting up and leaving? Like a crap party for example? I have. Maybe she was not really enjoying herself, and took that thought to next logical step.

Rude? Maybe/possibly/probably. Part of me applauds her honesty.

She was on her period?

I never heard of a group lunch before.

It sounds to me like someone or something upset her at the lunch but she was too embarrassed to explain about it.

You guys had a better lunch than her i reckon.

There's a possibility that she saw someone that she either doesn't like or has an awkward relationship with.