Was out getting lunch today with my girl and a guy friend of hers, and a few others. The guy was loud, cocky, kept throwing negs (they were almost just straight insults) at her, and she was eating it up. Maybe she didn't have the confidence to protest them, or maybe she liked the attention - not sure what it was.

How do I establish dominance here/make him look bad/get him the fuck off my territory in a more elegant way than punching his nose (I was getting close to doing this)?

I tried was just ignoring him and talking with her and others, which worked ok, but I wanted something better.

I feel like I need a way to make him look bad without making it obvious that I was getting pissed at him. Or maybe not - maybe I should just make it apparent that I'm annoyed.

Should I try to outdo him and be the 'life of the party' here, or is that too unnatural? What would you do here?

"Maybe she didn't have the confidence to protest them, or maybe she liked the attention - not sure what it was."

Watch your girlfriend better or ask her if she is ok. You have to see if the guy crosses the line or not.
If you girlfriend likes the attention then it's fine to ignore him. It wouldn't be good if you are ruin her "funny" day.

But if she is uncomfortable you have to protect her and safe her from the situation. Just give him the "stop it or I beat the shit out of you look". (if he asks you why you are looking just say: "You know why I'm looking, just stop it!"

If you don't have a bad boy look you can just say something like:
"HEY!! Stop it, ok!" or,
"Hey behave, this is my girlfriend you are talking to!"

Just show him the line and do it with a short command and go back to relaxed mode...
Don't use a question, don't try to compete, don't discuss and don't loose your composure.

If she's allready your girlfriend, don't act on the jealousy. It will make you seem needy and AFC. Just be chill about the whole situation, show her that you don't mind other guys flirting with her, because you trust her and are confident in yourself. In your mind, if he takes your girl, you will have hundred of other girls waiting in line for you.

Of course, DO NOT let him go too far either. She is YOUR girl, and he can't go on acting out on her. Don't be overly defensive or anything, but if you can tell that he bothers her, just make it clear that you are in charge, and that his behaviour is unacceptable.

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Alea iacta est - The die has been cast

I would personally call him out in front of everyone to chill out with the negative insults, keeping a adult and friendly tone. If it escalates it will show he is a douche.

If she enjoys the attention:
The big problem here is "she was eating it up". That tells me this guy is different and it is exciting / different for her. Unfortunately you can't do much in this situation in regards to keeping her unattracted to him. If you try to counter or play the same game he is playing, it's going to backfire and open channels for talk about you behind your back. I would not play the game, and just keep a close eye on her behavior, habbits, and what comes out of her mouth. You cant control the will of others and if she wants him there is nothing you can do but leave.

Lacks confidence:
This will be easy to spot as she should tell you how she feels when he is gone. (Which should be that she doesn't like the way he talks to her.) If you don't get this then shes enjoying the attention.

Poneal:

This guy you had lunch with with your girlfriend actively insulted her and you remained passive. That is not an attractive trait. Would you allow your little brother or sister to be treated the same way in front of you?

She may have been angry at the guy because he was a douche to her but then what is she going to think when her own boyfriend cannot even step in and control the situation.

I understand the last paragraph begs the question you've been asking but the answer is simple:

Step in and don't allow it to happen again. There is no correct way of handling it.

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"At the end of the day these are women's lives we're dealing with, not mere entertainment."

"We are what we repeatedly do. excellence therefore is a habit and not an act."